You searched for subject:(Stochastic optimal control).
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University of New South Wales
1.
Wu, Wei.
Limitations of dynamic programming approach: singularity and time inconsistency.
Degree: Mathematics & Statistics, 2016, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/56208 
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:40264/SOURCE02?view=true
► Two failures of the dynamic programming (DP) approach to the stochastic optimal control problem are investigated. The first failure arises when we wish to solve…
(more)
▼ Two failures of the dynamic programming (DP) approach to the
stochastic optimal control problem are investigated. The first failure arises when we wish to solve a class of certain singular
stochastic control problems in continuous time. It has been shown by Lasry and Lions (2000) that this difficulty can be overcome by introducing equivalent standard
stochastic control problems. To solve this class of singular
stochastic control problems, it remains to solve the equivalent standard
stochastic control problems. Since standard
stochastic control problems can be solved by applying the DP approach, this then solves the first failure. In the first part of the thesis, we clarify the idea of Lasry and Lions and extend their work to the case of controlled processes with jumps. This is particularly important in financial modelling where such processes are widely applied. For the purpose of application, we applied our result to an
optimal trade execution problem studied by Lasry and Lions (2007b). The second failure of the DP approach arises when we wish to solve a multiperiod portfolio selection problem in which a mean-standard-deviation type criterion (a non-separable criterion) is used. We formulate such a problem as a discrete time
stochastic control problem. By adapting a pseudo dynamic programming principle, we obtain a closed form
optimal strategy for investors whose risk tolerances are larger than a lower bound. As a consequence, we develop a multiperiod portfolio selection scheme. The analysis is performed in the market of risky assets only, however, we allow both market transitions and intermediate cash injections and offtakes. This work provides a good basis for future studies of portfolio selection problems with selection criteria chosen from the class of translation-invariant and positive-homogeneous risk measures.
Advisors/Committee Members: Goldys, Beniamin, The University of Sydney, Penev, Spiridon , Mathematics & Statistics, Faculty of Science, UNSW.
Subjects/Keywords: Stochastic optimal control; Dynamic programming; Stochastic control
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APA (6th Edition):
Wu, W. (2016). Limitations of dynamic programming approach: singularity and time inconsistency. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/56208 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:40264/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Wu, Wei. “Limitations of dynamic programming approach: singularity and time inconsistency.” 2016. Doctoral Dissertation, University of New South Wales. Accessed September 15, 2019.
http://handle.unsw.edu.au/1959.4/56208 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:40264/SOURCE02?view=true.
MLA Handbook (7th Edition):
Wu, Wei. “Limitations of dynamic programming approach: singularity and time inconsistency.” 2016. Web. 15 Sep 2019.
Vancouver:
Wu W. Limitations of dynamic programming approach: singularity and time inconsistency. [Internet] [Doctoral dissertation]. University of New South Wales; 2016. [cited 2019 Sep 15].
Available from: http://handle.unsw.edu.au/1959.4/56208 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:40264/SOURCE02?view=true.
Council of Science Editors:
Wu W. Limitations of dynamic programming approach: singularity and time inconsistency. [Doctoral Dissertation]. University of New South Wales; 2016. Available from: http://handle.unsw.edu.au/1959.4/56208 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:40264/SOURCE02?view=true
Boston University
2.
Ren, Dan.
Stochastic optimization and applications in finance.
Degree: PhD, Mathematics & Statistics, 2013, Boston University
URL: http://hdl.handle.net/2144/13130
► My PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts:…
(more)
▼ My PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts: the first part studies an optimal stopping problem, and the second part studies an optimal control problem.
The first topic considers a one-dimensional transient and downwards drifting diffusion process X, and detects the optimal times of a random time(denoted as ρ). In particular, we consider two classes of random times: (1) the last time when the process exits a certain level l; (2) the time when the process reaches its maximum. For each random time, we solve the optimization problem
infτ E[λ(τ- ρ)+ +(1-λ)(ρ - τ)+]
overall all stopping times. For the last exit time, the process should stop optimally when it runs below some fixed level k the first time, where k is the solution of an explicit defined equation. For the ultimate maximum time, the process should stop optimally when it runs below a boundary which is the maximal positive solution (if exists) of a first-order ordinary differential equation which lies below the line λs for all s > 0 .
The second topic solves an optimal consumption and investment problem for a risk-averse investor who is sensitive to declines than to increases of standard living (i.e., the investor is loss averse), and the investment opportunities are constant. We use the tools of stochastic control and duality methods to solve the resulting free-boundary problem in an infinite time horizon. Briefly, the investor consumes constantly when holding a moderate amount of wealth. In bliss time, the investor increases the consumption so that the consumption-wealth ratio reaches some fixed minimum level; in gloom time, the investor decreases the consumption gradually. Moreover, high loss aversion tends to raise the consumption-wealth ratio, but cut the investment-wealth ratio overall.
Subjects/Keywords: Mathematics; Financial mathematics; Optimal consumption; Optimal control; Optimal stopping; Stochastic optimization
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APA (6th Edition):
Ren, D. (2013). Stochastic optimization and applications in finance. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/13130
Chicago Manual of Style (16th Edition):
Ren, Dan. “Stochastic optimization and applications in finance.” 2013. Doctoral Dissertation, Boston University. Accessed September 15, 2019.
http://hdl.handle.net/2144/13130.
MLA Handbook (7th Edition):
Ren, Dan. “Stochastic optimization and applications in finance.” 2013. Web. 15 Sep 2019.
Vancouver:
Ren D. Stochastic optimization and applications in finance. [Internet] [Doctoral dissertation]. Boston University; 2013. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/2144/13130.
Council of Science Editors:
Ren D. Stochastic optimization and applications in finance. [Doctoral Dissertation]. Boston University; 2013. Available from: http://hdl.handle.net/2144/13130
University of Southern California
3.
Theodorou, Evangelos A.
Iterative path integral stochastic optimal control: theory
and applications to motor control.
Degree: PhD, Computer Science, 2011, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/468575/rec/3674
► Motivated by the limitations of current optimal control and reinforcement learning methods in terms of their efficiency and scalability, this thesis proposes an iterative stochastic…
(more)
▼ Motivated by the limitations of current
optimal
control and reinforcement learning methods in terms of their
efficiency and scalability, this thesis proposes an iterative
stochastic optimal control approach based on the generalized path
integral formalism. More precisely, we suggest the use of the
framework of
stochastic optimal control with path integrals to
derive a novel approach to RL with parameterized policies. While
solidly grounded in value function estimation and
optimal control
based on the
stochastic Hamilton Jacobi Bellman (HJB) equation,
policy improvements can be transformed into an approximation
problem of a path integral which has no open algorithmic parameters
other than the exploration noise. The resulting algorithm can be
conceived of as model-based, semi-model-based, or even model free,
depending on how the learning problem is structured. The new
algorithm, Policy Improvement with Path Integrals (PI2),
demonstrates interesting similarities with previous RL research in
the framework of probability matching and provides intuition why
the slightly heuristically motivated probability matching approach
can actually perform well. Applications to high dimensional robotic
systems are presented for a variety of tasks that require
optimal
planning and gain scheduling.; In addition to the work on
generalized path integral
stochastic optimal control, in this
thesis we extend model based iterative
optimal control algorithms
to the
stochastic setting. More precisely we derive the
Differential Dynamic Programming algorithm for
stochastic systems
with state and
control multiplicative noise. Finally, in the last
part of this thesis, model based iterative
optimal control methods
are applied to bio-mechanical models of the index finger with the
goal to find the underlying tendon forces applied for the movements
of, tapping and flexing.
Advisors/Committee Members: Schaal, Stefan (Committee Chair), Valero-Cuevas, Francisco (Committee Member), Sukhatme, Gaurav S. (Committee Member), Todorov, Emo (Committee Member), Schweighofer, Nicolas (Committee Member).
Subjects/Keywords: stochastic optimal control; reinforcement learning,; robotics
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APA (6th Edition):
Theodorou, E. A. (2011). Iterative path integral stochastic optimal control: theory
and applications to motor control. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/468575/rec/3674
Chicago Manual of Style (16th Edition):
Theodorou, Evangelos A. “Iterative path integral stochastic optimal control: theory
and applications to motor control.” 2011. Doctoral Dissertation, University of Southern California. Accessed September 15, 2019.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/468575/rec/3674.
MLA Handbook (7th Edition):
Theodorou, Evangelos A. “Iterative path integral stochastic optimal control: theory
and applications to motor control.” 2011. Web. 15 Sep 2019.
Vancouver:
Theodorou EA. Iterative path integral stochastic optimal control: theory
and applications to motor control. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2019 Sep 15].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/468575/rec/3674.
Council of Science Editors:
Theodorou EA. Iterative path integral stochastic optimal control: theory
and applications to motor control. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/468575/rec/3674
Université de Grenoble
4.
Salch, Alexandre.
Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience.
Degree: Docteur es, Mathématiques et informatique, 2013, Université de Grenoble
URL: http://www.theses.fr/2013GRENM062
► Le sujet de cette thèse est l'étude de systèmes de production avec impatience. Ces systèmes sont modélisés comme des problèmes d'ordonnancement stochastiques avec des dates…
(more)
▼ Le sujet de cette thèse est l'étude de systèmes de production avec impatience. Ces systèmes sont modélisés comme des problèmes d'ordonnancement stochastiques avec des dates d'échéance. Dans la littérature, peu de résultats existent sur le contrôle optimal de ce genre de systèmes. C'est dans ce cadre que s'inscrit cette thèse. Nous considérons un système générique avec une machine, sur laquelle des tâches sont à exécuter. Les durées d'exécution, les dates d'échéance (ou durées d'impatience) et les dates de disponibilité des tâches sont des variables aléatoires. À chaque tâche est associé un poids et l'objectif est de minimiser l'espérance du nombre pondéré de tâches en retard. Dans notre étude, nous utilisons différentes modélisations, rendant compte des différentes contraintes régissant des systèmes réels. Notamment, nous faisons la différence entre l'impatience, le fait d'avoir attendu trop longtemps, et l'abandon, le fait de quitter le système suite à l'impatience. Dans la classe des politiques statiques, nous donnons des ordonnancements optimaux pour des problèmes avec impatience. Dans la classe des politiques dynamiques avec préemption, nous donnons de nouvelles conditions garantissant l'optimalité d'une politique stricte pour des problèmes avec abandon et nous proposons une heuristique plus efficace que celles que l'on trouve dans la littérature. Enfin, nous explorons des variantes et des extensions de ces problèmes, lorsque le système comporte plusieurs machines et lorsque la préemption n'est pas autorisée.
In this thesis, production systems facing abandonments are studied. These problems are modeled as stochastic scheduling problems with due dates. In the literature, few results exist concerning the optimal control of such systems. This thesis aims at providing optimal control policies for systems with impatience. We consider a generic system with a single machine, on which jobs have to be processed. Processing times, due dates (or patience time) and release dates are random variables. A weight is associated to each job and the objective is to minimize the expected weighted number of late jobs. In our study, we use different models, taking into account the specific features of real life problems. For example, we make a difference between impatience, when a customer has been waiting for too long, and abandonment, when a customer leaves the system after getting impatient. In the class of static list scheduling policies, we provide optimal schedules for problems with impatience. In the class of preemptive dynamic policies, we specify conditions under which a strict priority rule is optimal and we give a new heuristic, both extending previous results from the literature. We study variants and extensions of these problems, when several machines are available or when preemption is not authorized.
Advisors/Committee Members: Gayon, Jean-Philippe (thesis director), Lemaire, Pierre (thesis director).
Subjects/Keywords: Ordonnancement; Contrôle optimal; Aléatoire; Scheduling; Optimal control; Stochastic; 004
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APA ·
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MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Salch, A. (2013). Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2013GRENM062
Chicago Manual of Style (16th Edition):
Salch, Alexandre. “Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience.” 2013. Doctoral Dissertation, Université de Grenoble. Accessed September 15, 2019.
http://www.theses.fr/2013GRENM062.
MLA Handbook (7th Edition):
Salch, Alexandre. “Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience.” 2013. Web. 15 Sep 2019.
Vancouver:
Salch A. Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience. [Internet] [Doctoral dissertation]. Université de Grenoble; 2013. [cited 2019 Sep 15].
Available from: http://www.theses.fr/2013GRENM062.
Council of Science Editors:
Salch A. Ordonnancement stochastique avec impatience : Stochastic scheduling with impatience. [Doctoral Dissertation]. Université de Grenoble; 2013. Available from: http://www.theses.fr/2013GRENM062
University of Manchester
5.
Blair, James.
Modelling approaches for optimal liquidation under a
limit-order book structure.
Degree: 2016, University of Manchester
URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:300421
► This thesis introduces a selection of models for optimal execution of financial assets at the tactical level. As opposed to optimal scheduling, which defines a…
(more)
▼ This thesis introduces a selection of models for
optimal execution of financial assets at the tactical level. As
opposed to optimal scheduling, which defines a trading schedule for
the trader, this thesis investigates how the trader should interact
with the order book. If a trader is aggressive he will execute his
order using market orders, which will negatively feedback on his
execution price through market impact. Alternatively, the models we
focus on consider a passive trader who places limit orders into the
limit-order book and waits for these orders to be filled by market
orders from other traders. We assume these models do not exhibit
market impact. However, given we await market orders from other
participants to fill our limit orders a new risk is borne:
execution risk.We begin with an extension of Guéant et al. (2012b)
who through the use of an exponential utility, standard Brownian
motion, and an absolute decay parameter were able to cleverly build
symmetry into their model which significantly reduced the
complexity. Our model consists of geometric Brownian motion (and
mean-reverting processes) for the asset price, a proportional
control parameter (the additional amount we ask for the asset), and
a proportional decay parameter, implying that the symmetry found in
Guéant et al. (2012b) no longer exists. This novel combination
results in asset-dependent trading strategies, which to our
knowledge is a unique concept in this framework of literature.
Detailed asymptotic analyses, coupled with advanced numerical
techniques (informing the asymptotics) are exploited to extract the
relevant dynamics, before looking at further extensions using
similar methods.We examine our above mentioned framework, as well
as that of Guéant et al. (2012), for a trader who has a basket of
correlated assets to liquidate. This leads to a higher-dimensional
model which increases the complexity of both numerically solving
the problem and asymptotically examining it. The solutions we
present are of interest, and comparable with Markowitz portfolio
theory. We return to our framework of a single underlying and
consider four extensions: a stochastic volatility model which
results in an added dimension to the problem, a constrained
optimisation problem in which the control has an explicit lower
bound, changing the exponential intensity to a power intensity
which results in a reformulation as a singular stochastic control
problem, and allowing the trader to trade using both market orders
and limit orders resulting in a free-boundary problem.We complete
the study with an empirical analysis using limit-order book data
which contains multiple levels of the book. This involves a novel
calibration of the intensity functions which represent the
limit-order book, before backtesting and analysing the performance
of the strategies.
NA
NA
Advisors/Committee Members: JOHNSON, PAUL PV, Duck, Peter, Johnson, Paul.
Subjects/Keywords: Stochastic Optimal Control; Mathematical Finance; Optimal Execution; Algorithmic Trading
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Blair, J. (2016). Modelling approaches for optimal liquidation under a
limit-order book structure. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:300421
Chicago Manual of Style (16th Edition):
Blair, James. “Modelling approaches for optimal liquidation under a
limit-order book structure.” 2016. Doctoral Dissertation, University of Manchester. Accessed September 15, 2019.
http://www.manchester.ac.uk/escholar/uk-ac-man-scw:300421.
MLA Handbook (7th Edition):
Blair, James. “Modelling approaches for optimal liquidation under a
limit-order book structure.” 2016. Web. 15 Sep 2019.
Vancouver:
Blair J. Modelling approaches for optimal liquidation under a
limit-order book structure. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2019 Sep 15].
Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:300421.
Council of Science Editors:
Blair J. Modelling approaches for optimal liquidation under a
limit-order book structure. [Doctoral Dissertation]. University of Manchester; 2016. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:300421
University of Manchester
6.
Blair, James.
Modelling approaches for optimal liquidation under a limit-order book structure.
Degree: PhD, 2016, University of Manchester
URL: https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689582
► This thesis introduces a selection of models for optimal execution of financial assets at the tactical level. As opposed to optimal scheduling, which defines a…
(more)
▼ This thesis introduces a selection of models for optimal execution of financial assets at the tactical level. As opposed to optimal scheduling, which defines a trading schedule for the trader, this thesis investigates how the trader should interact with the order book. If a trader is aggressive he will execute his order using market orders, which will negatively feedback on his execution price through market impact. Alternatively, the models we focus on consider a passive trader who places limit orders into the limit-order book and waits for these orders to be filled by market orders from other traders. We assume these models do not exhibit market impact. However, given we await market orders from other participants to fill our limit orders a new risk is borne: execution risk. We begin with an extension of Guéant et al. (2012b) who through the use of an exponential utility, standard Brownian motion, and an absolute decay parameter were able to cleverly build symmetry into their model which significantly reduced the complexity. Our model consists of geometric Brownian motion (and mean-reverting processes) for the asset price, a proportional control parameter (the additional amount we ask for the asset), and a proportional decay parameter, implying that the symmetry found in Guéant et al. (2012b) no longer exists. This novel combination results in asset-dependent trading strategies, which to our knowledge is a unique concept in this framework of literature. Detailed asymptotic analyses, coupled with advanced numerical techniques (informing the asymptotics) are exploited to extract the relevant dynamics, before looking at further extensions using similar methods. We examine our above mentioned framework, as well as that of Guéant et al. (2012), for a trader who has a basket of correlated assets to liquidate. This leads to a higher-dimensional model which increases the complexity of both numerically solving the problem and asymptotically examining it. The solutions we present are of interest, and comparable with Markowitz portfolio theory. We return to our framework of a single underlying and consider four extensions: a stochastic volatility model which results in an added dimension to the problem, a constrained optimisation problem in which the control has an explicit lower bound, changing the exponential intensity to a power intensity which results in a reformulation as a singular stochastic control problem, and allowing the trader to trade using both market orders and limit orders resulting in a free-boundary problem. We complete the study with an empirical analysis using limit-order book data which contains multiple levels of the book. This involves a novel calibration of the intensity functions which represent the limit-order book, before backtesting and analysing the performance of the strategies.
Subjects/Keywords: 519.5; Stochastic Optimal Control; Mathematical Finance; Optimal Execution; Algorithmic Trading
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Blair, J. (2016). Modelling approaches for optimal liquidation under a limit-order book structure. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689582
Chicago Manual of Style (16th Edition):
Blair, James. “Modelling approaches for optimal liquidation under a limit-order book structure.” 2016. Doctoral Dissertation, University of Manchester. Accessed September 15, 2019.
https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689582.
MLA Handbook (7th Edition):
Blair, James. “Modelling approaches for optimal liquidation under a limit-order book structure.” 2016. Web. 15 Sep 2019.
Vancouver:
Blair J. Modelling approaches for optimal liquidation under a limit-order book structure. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2019 Sep 15].
Available from: https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689582.
Council of Science Editors:
Blair J. Modelling approaches for optimal liquidation under a limit-order book structure. [Doctoral Dissertation]. University of Manchester; 2016. Available from: https://www.research.manchester.ac.uk/portal/en/theses/modelling-approaches-for-optimal-liquidation-under-a-limitorder-book-structure(a7c23b2a-e2f8-4b4a-9865-8783d9837198).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689582
University of Ottawa
7.
Iolov, Alexandre V.
Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
.
Degree: 2016, University of Ottawa
URL: http://hdl.handle.net/10393/34866
► This thesis solves estimation and control problems in computational neuroscience, mathematically dealing with the first-passage times of diffusion stochastic processes. We first derive estimation algorithms…
(more)
▼ This thesis solves estimation and control problems in computational
neuroscience, mathematically dealing with the first-passage times of diffusion
stochastic processes. We first derive estimation algorithms for model parameters
from first-passage time observations, and then we derive algorithms for the
control of first-passage times. Finally, we solve an optimal design
problem which combines elements of the first two: we ask how to elicit
first-passage times such as to facilitate model estimation based on said
first-passage observations.
The main mathematical tools used are the Fokker-Planck partial differential
equation for evolution of probability densities, the Hamilton-Jacobi-Bellman
equation of optimal control and the adjoint optimization principle from optimal
control theory.
The focus is on developing computational schemes for the
solution of the problems. The schemes are implemented and are tested for a wide
range of parameters.
Subjects/Keywords: Stochastic Optimal Control;
Stochastic Leaky Integrate-and-Fire Neural Model;
Optimal Design;
First-Passage Times
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APA ·
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MLA ·
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CSE |
Export
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Manager
APA (6th Edition):
Iolov, A. V. (2016). Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
. (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/34866
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Iolov, Alexandre V. “Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
.” 2016. Thesis, University of Ottawa. Accessed September 15, 2019.
http://hdl.handle.net/10393/34866.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Iolov, Alexandre V. “Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
.” 2016. Web. 15 Sep 2019.
Vancouver:
Iolov AV. Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
. [Internet] [Thesis]. University of Ottawa; 2016. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/10393/34866.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Iolov AV. Parameter Estimation, Optimal Control and Optimal Design in Stochastic Neural Models
. [Thesis]. University of Ottawa; 2016. Available from: http://hdl.handle.net/10393/34866
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
8.
Filo, Maurice George.
Topics in Stochastic Stability, Optimal Control and Estimation Theory.
Degree: 2018, University of California – eScholarship, University of California
URL: http://www.escholarship.org/uc/item/7nh0k0dp
► This dissertation consists of four parts that revolve around structured stochastic uncertainty and optimal control/estimation theory.In the first part, we consider the continuous-time setting of…
(more)
▼ This dissertation consists of four parts that revolve around structured stochastic uncertainty and optimal control/estimation theory.In the first part, we consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective is to characterize the conditions of Mean-Square Stability (MSS) using a purely input-output approach. This approach leads to uncovering new tools such as stochastic block diagrams. Various stochastic interpretations are considered, such as It\=o and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a matrix operator that takes different forms when different stochastic interpretations are considered. The second part applies the developed theory to analyze the mean-square stability and performance of stochastic cochlear models. The analysis is carried out for a generalized class of biomechanical models of the cochlea, that is formulated as a stochastic spatially distributed system, by allowing stochastic spatio-temporal perturbations within the cochlear amplifier. The simulation-free analysis explains the underlying mechanisms that give rise to cochlear instabilities such as spontaneous otoacoustic emissions and/or tinnitus. Furthermore, nonlinear stochastic simulations are carried out to validate the predictions of the theoretical analysis. The third part revisits the development of numerical methods to solve optimal control problems using a function-space approach. This approach has the advantage of unifying the framework upon which the various (existing) numerical methods are based on. In fact, this approach motivates the definition of various system and projection operators that make the derivations conceptually transparent. Furthermore, the function-space approach builds useful geometric intuitions that inspire the development of new projection-based methods.In the last part, we propose a methodology of optimal path design for sensors through a distributed environment. We consider time-limited scenarios where the sensors can only make a small number of measurements, but where some portion of a physics-based model is available for the field of interest (such as temperature). We consider both point-wise and tomographic sensors. The main idea is to recast the sensor path planning problem as a deterministic optimal control problem to minimize metrics related to the optimal estimation error covariance.
Subjects/Keywords: Engineering; Acoustic Tomography; Cochlea; Optimal Control; Optimal Estimation; Stochastic Stability; Stochastic Uncertainty
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APA (6th Edition):
Filo, M. G. (2018). Topics in Stochastic Stability, Optimal Control and Estimation Theory. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/7nh0k0dp
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Filo, Maurice George. “Topics in Stochastic Stability, Optimal Control and Estimation Theory.” 2018. Thesis, University of California – eScholarship, University of California. Accessed September 15, 2019.
http://www.escholarship.org/uc/item/7nh0k0dp.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Filo, Maurice George. “Topics in Stochastic Stability, Optimal Control and Estimation Theory.” 2018. Web. 15 Sep 2019.
Vancouver:
Filo MG. Topics in Stochastic Stability, Optimal Control and Estimation Theory. [Internet] [Thesis]. University of California – eScholarship, University of California; 2018. [cited 2019 Sep 15].
Available from: http://www.escholarship.org/uc/item/7nh0k0dp.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Filo MG. Topics in Stochastic Stability, Optimal Control and Estimation Theory. [Thesis]. University of California – eScholarship, University of California; 2018. Available from: http://www.escholarship.org/uc/item/7nh0k0dp
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Georgia Tech
9.
Exarchos, Ioannis.
Stochastic optimal control - a forward and backward sampling approach.
Degree: PhD, Aerospace Engineering, 2017, Georgia Tech
URL: http://hdl.handle.net/1853/59263
► Stochastic optimal control has seen significant recent development, motivated by its success in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and…
(more)
▼ Stochastic optimal control has seen significant recent development, motivated by its success in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and financial engineering. Despite the many theoretical and algorithmic advancements that made such a success possible, several obstacles remain; most notable are (i) the mitigation of the curse of dimensionality inherent in
optimal control problems, (ii) the design of efficient algorithms that allow for fast, online computation, and (iii) the expansion of the class of
optimal control problems that can be addressed by algorithms in engineering practice. The aim of this dissertation is the development of a learning
stochastic control framework which capitalizes on the innate relationship between certain nonlinear partial differential equations (PDEs) and forward and backward
stochastic differential equations (FBSDEs), demonstrated by a nonlinear version of the Feynman-Kac lemma. By means of this lemma, we are able to obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Bellman PDE, expressed in form of a system of decoupled FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. We present a novel discretization scheme for FBSDEs, and enhance the resulting algorithm with importance sampling, thereby constructing an iterative scheme that is capable of learning the
optimal control without an initial guess, even in systems with highly nonlinear, underactuated dynamics. The framework we develop within this dissertation addresses several classes of
stochastic optimal control, such as L2, L1, risk sensitive
control, as well as some classes of differential games, in both fixed-final-time as well as first-exit settings.
Advisors/Committee Members: Tsiotras, Panagiotis (advisor), Theodorou, Evangelos A. (advisor), Haddad, Wassim M. (committee member), Zhou, Haomin (committee member), Popescu, Ionel (committee member).
Subjects/Keywords: Stochastic optimal control; Forward and backward stochastic differential equations
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APA (6th Edition):
Exarchos, I. (2017). Stochastic optimal control - a forward and backward sampling approach. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59263
Chicago Manual of Style (16th Edition):
Exarchos, Ioannis. “Stochastic optimal control - a forward and backward sampling approach.” 2017. Doctoral Dissertation, Georgia Tech. Accessed September 15, 2019.
http://hdl.handle.net/1853/59263.
MLA Handbook (7th Edition):
Exarchos, Ioannis. “Stochastic optimal control - a forward and backward sampling approach.” 2017. Web. 15 Sep 2019.
Vancouver:
Exarchos I. Stochastic optimal control - a forward and backward sampling approach. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/1853/59263.
Council of Science Editors:
Exarchos I. Stochastic optimal control - a forward and backward sampling approach. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/59263
Washington University in St. Louis
10.
Qi, Ji.
Control of Deterministic and Stochastic Linear Ensemble Systems.
Degree: PhD, Electrical & Systems Engineering, 2014, Washington University in St. Louis
URL: https://openscholarship.wustl.edu/eng_etds/71
► The behavior of physical, chemical, and biological systems can exhibit significant sensitivity to uncertainty or variation in system parameters. This factor arises in practical…
(more)
▼ The behavior of physical, chemical, and biological systems can exhibit significant sensitivity to uncertainty or variation in system parameters. This factor arises in practical
control problems in many areas of science and engineering when there is uncertainty in the parameters of a single
control system, or when a collection of structurally similar systems with variations in common parameters must be steered using a common
control signal. Analysis of these cases has given rise to the
subject of ensemble
control, which was motivated by practical
control design problems in the fields of nuclear magnetic resonance spectroscopy and imaging, neuroscience, and sensorless robotic manipulation. This dissertation focuses on the investigation of fundamental properties and the development of
optimal controls for deterministic and
stochastic linear ensemble systems. Although the ensemble controllability for deterministic linear ensemble systems has been characterized in previous studies, explicit controllability conditions remain undiscovered. In this dissertation, explicit controllability conditions for a class of time-invariant linear ensemble systems with linear parameter variation are constructed. This class of ensemble
control systems arises from practical engineering and physical applications, such as the transport of quantum particles and
control of uncertain harmonic systems. The construction is based on the notion of polynomial approximation, and the conditions are related to the rank of the system matrices and are easy to verify. In addition to the study of deterministic ensemble
control systems, we extend our work to a
stochastic case where the ensemble systems are
subject to random dynamic disturbances. Such disturbances can greatly affect the behavior of systems, which can become particularly challenging to
control in a desired manner as a result, especially when feedback cannot be used to attenuate disturbances. We study
optimal steering problems involving
stochastic linear ensemble systems driven by Gaussian noise and Poisson counters. In particular, we seek to minimize the statistical objectives of the mean square error (MSE) and the error in the mean of the terminal state of the ensemble with respect to the desired state.
Advisors/Committee Members: Hiro Mukai, Heinz Schaettler, Istvan Kiss.
Subjects/Keywords: controllability; ensemble control; optimal control; polynomial approxiamtion; stochastic; Engineering
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APA ·
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MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Qi, J. (2014). Control of Deterministic and Stochastic Linear Ensemble Systems. (Doctoral Dissertation). Washington University in St. Louis. Retrieved from https://openscholarship.wustl.edu/eng_etds/71
Chicago Manual of Style (16th Edition):
Qi, Ji. “Control of Deterministic and Stochastic Linear Ensemble Systems.” 2014. Doctoral Dissertation, Washington University in St. Louis. Accessed September 15, 2019.
https://openscholarship.wustl.edu/eng_etds/71.
MLA Handbook (7th Edition):
Qi, Ji. “Control of Deterministic and Stochastic Linear Ensemble Systems.” 2014. Web. 15 Sep 2019.
Vancouver:
Qi J. Control of Deterministic and Stochastic Linear Ensemble Systems. [Internet] [Doctoral dissertation]. Washington University in St. Louis; 2014. [cited 2019 Sep 15].
Available from: https://openscholarship.wustl.edu/eng_etds/71.
Council of Science Editors:
Qi J. Control of Deterministic and Stochastic Linear Ensemble Systems. [Doctoral Dissertation]. Washington University in St. Louis; 2014. Available from: https://openscholarship.wustl.edu/eng_etds/71
University of Notre Dame
11.
Matthew Zyskowski.
Cost Density-Shaping for Stochastic Optimal
Control</h1>.
Degree: PhD, Electrical Engineering, 2010, University of Notre Dame
URL: https://curate.nd.edu/show/r207tm73247
► In stochastic optimal control theory, the complete specification of the probability density function of the random cost functional might be considered the most a…
(more)
▼ In
stochastic optimal control theory, the
complete specification of the probability density function of the
random cost functional might be considered the most a designer can
do when formulating an
optimal control law. The field of cost
cumulant controls has made considerable advances towards this
capability in the past few decades, largely because of the
advantage gained from controlling the cost cumulants instead of the
cost moments. However, current cost cumulant
control paradigms have
left the deliberate specification of the probability density
function for the random cost outside the designer’s direct
influence. The ability to design
control laws upon the desired
shape and location of the cost density would be highly valuable to
control engineers, since there is evidence that the shape of the
cost density under high-performance controllers directly
corresponds to the resulting closed-loop system behavior.
This dissertation proposes
a Multiple-Cumulant Cost Density-Shaping (MCCDS) optimization
problem for the LQG framework. The
control solution to the MCCDS
optimization is derived using dynamic programming techniques; it is
the finite-horizon, linear state-feedback
control that minimizes a
smooth, convex, scalar function of arbitrarily-many initial cost
cumulants and target initial cost cumulants. The MCCDS theory is
shown to generalize the Linear Quadratic Gaussian (LQG), “k Cost
Cumulant” (kCC), and Risk-Sensitive (RS)
control paradigms for zero
targets and linear performance indices. Additionally, the MCCDS
framework enables the minimization of well-known distance functions
between the cost density and a target cost density, such as the
Kullback-Leibler Divergence, Bhattacharyya Distance, and the
Hellinger Distance. The
finite-horizon MCCDS
control is extended to the infinite-horizon in
this dissertation. Other areas of investigation include MCCDS
performance index construction, cost density-shaping minimax and
Nash games, and a Statistical Target Selection (STS) iterative
procedure for
control design. Together MCCDS and STS enable the
design of
control laws with optimality among a family of target
cost densities, which might be regarded as a new approach to robust
LQG
control design. For structures excited by seismic disturbances,
numerical experiments show that the MCCDS controls identified thru
STS can achieve greater vibration suppression than nominal kCC
controllers, without any compromise to robust
stability.
Advisors/Committee Members: Dr. Ron Diersing, Committee Member, Dr. Peter Bauer, Committee Member, Dr. Vijay Gupta, Committee Member, Dr. Yih-Fang Huang, Committee Member, Dr. Panos Antsaklis, Committee Chair.
Subjects/Keywords: cost density-shaping; stochastic optimal control; LQG; cost cumulant control
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zyskowski, M. (2010). Cost Density-Shaping for Stochastic Optimal
Control</h1>. (Doctoral Dissertation). University of Notre Dame. Retrieved from https://curate.nd.edu/show/r207tm73247
Chicago Manual of Style (16th Edition):
Zyskowski, Matthew. “Cost Density-Shaping for Stochastic Optimal
Control</h1>.” 2010. Doctoral Dissertation, University of Notre Dame. Accessed September 15, 2019.
https://curate.nd.edu/show/r207tm73247.
MLA Handbook (7th Edition):
Zyskowski, Matthew. “Cost Density-Shaping for Stochastic Optimal
Control</h1>.” 2010. Web. 15 Sep 2019.
Vancouver:
Zyskowski M. Cost Density-Shaping for Stochastic Optimal
Control</h1>. [Internet] [Doctoral dissertation]. University of Notre Dame; 2010. [cited 2019 Sep 15].
Available from: https://curate.nd.edu/show/r207tm73247.
Council of Science Editors:
Zyskowski M. Cost Density-Shaping for Stochastic Optimal
Control</h1>. [Doctoral Dissertation]. University of Notre Dame; 2010. Available from: https://curate.nd.edu/show/r207tm73247
University of Manchester
12.
Martyr, Randall.
Optimal prediction games in local electricity
markets.
Degree: 2015, University of Manchester
URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:281877
► Local electricity markets can be defined broadly as "future electricity market designs involving domestic customers, demand-side response and energy storage". Like current deregulated electricity markets,…
(more)
▼ Local electricity markets can be defined broadly as
"future electricity market designs involving domestic customers,
demand-side response and energy storage". Like current deregulated
electricity markets, these localised derivations present specific
stochastic optimisation problems in which the dynamic and random
nature of the market is intertwined with the physical needs of its
participants. Moreover, the types of contracts and constraints in
this setting are such that ``games'' naturally emerge between the
agents. Advanced modelling techniques beyond classical mathematical
finance are therefore key to their analysis. This thesis aims to
study contracts in these local electricity markets using the
mathematical theories of
stochastic optimal control and
games.Chapter 1 motivates the research, provides an overview of the
electricity market in Great Britain, and summarises the content of
this thesis. It introduces three problems which are studied later
in the thesis: a simple
control problem involving demand-side
management for domestic customers, and two examples of games within
local electricity markets, one of them involving energy storage.
Chapter 2 then reviews the literature most relevant to the topics
discussed in this work.Chapter 3 investigates how electric space
heating loads can be made responsive to time varying prices in an
electricity spot market. The problem is formulated mathematically
within the framework of deterministic
optimal control, and is
analysed using methods such as Pontryagin's Maximum Principle and
Dynamic Programming. Numerical simulations are provided to
illustrate how the
control strategies perform on real market
data.The problem of Chapter 3 is reformulated in Chapter 4 as one
of
optimal switching in discrete-time. A martingale approach is
used to establish the existence of an
optimal strategy in a very
general setup, and also provides an algorithm for computing the
value function and the
optimal strategy. The theory is exemplified
by a numerical example for the motivating problem. Chapter 5 then
continues the study of finite horizon
optimal switching problems,
but in continuous time. It also uses martingale methods to prove
the existence of an
optimal strategy in a fairly general
model.Chapter 6 introduces a mathematical model for a game
contingent claim between an electricity supplier and generator
described in the introduction. A theory for using
optimal switching
to solve such games is developed and subsequently evidenced by a
numerical example. An
optimal switching formulation of the
aforementioned game contingent claim is provided for an abstract
Markovian model of the electricity market.The final chapter studies
a balancing services contract between an electricity transmission
system operator (SO) and the owner of an electric energy storage
device (battery operator or BO). The objectives of the SO and BO
are combined in a non-zero sum
stochastic differential game where
one player (BO) uses a classic
control with continuous effects,
whereas the other player (SO) uses an impulse…
Advisors/Committee Members: PESKIR, GORAN G, Moriarty, John, Peskir, Goran.
Subjects/Keywords: optimal control; stochastic control; optimal stopping; stochastic games; optimal switching; optimal impulse control; power system economics; electricity markets; contracts for difference; electricity market reform; balancing services; demand response; energy storage
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Martyr, R. (2015). Optimal prediction games in local electricity
markets. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:281877
Chicago Manual of Style (16th Edition):
Martyr, Randall. “Optimal prediction games in local electricity
markets.” 2015. Doctoral Dissertation, University of Manchester. Accessed September 15, 2019.
http://www.manchester.ac.uk/escholar/uk-ac-man-scw:281877.
MLA Handbook (7th Edition):
Martyr, Randall. “Optimal prediction games in local electricity
markets.” 2015. Web. 15 Sep 2019.
Vancouver:
Martyr R. Optimal prediction games in local electricity
markets. [Internet] [Doctoral dissertation]. University of Manchester; 2015. [cited 2019 Sep 15].
Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:281877.
Council of Science Editors:
Martyr R. Optimal prediction games in local electricity
markets. [Doctoral Dissertation]. University of Manchester; 2015. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:281877
King Abdullah University of Science and Technology
13.
Caballero, Renzo.
Stochastic Optimal Control of Renewable Energy.
Degree: 2019, King Abdullah University of Science and Technology
URL: http://hdl.handle.net/10754/655846
► Uruguay is a pioneer in the use of renewable sources of energy and can usually satisfy its total demand from renewable sources. Control and optimization…
(more)
▼ Uruguay is a pioneer in the use of renewable sources of energy and can usually satisfy its total demand from renewable sources. Control and optimization of the system is complicated by half of the installed power - wind and solar sources - be- ing non-controllable with high uncertainty and variability. In this work we present a novel optimization technique for efficient use of the production facilities. The dy- namical system is stochastic, and we deal with its non-Markovian dynamics through a Lagrangian relaxation. Continuous-time optimal control and value function are found from the solution to a sequence of Hamilton-Jacobi-Bellman partial differential equations associated with the system. We introduce a monotone scheme to avoid spurious oscillations in the numerical solution and apply the technique to a number of examples taken from the Uruguayan grid. We use parallelization and change of variables to reduce the computational times. Finally, we study the usefulness of extra system storage capacity offered by batteries.
Subjects/Keywords: optimal control; renewable energy; Hamilton-Jacobi-Bellman; wind power optimiztion; stochastic optimal control; optimal energy dispatch
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APA ·
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APA (6th Edition):
Caballero, R. (2019). Stochastic Optimal Control of Renewable Energy. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/655846
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Caballero, Renzo. “Stochastic Optimal Control of Renewable Energy.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed September 15, 2019.
http://hdl.handle.net/10754/655846.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Caballero, Renzo. “Stochastic Optimal Control of Renewable Energy.” 2019. Web. 15 Sep 2019.
Vancouver:
Caballero R. Stochastic Optimal Control of Renewable Energy. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/10754/655846.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Caballero R. Stochastic Optimal Control of Renewable Energy. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/655846
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Georgia Tech
14.
Li, Wuchen.
A study of stochastic differential equations and Fokker-Planck equations with applications.
Degree: PhD, Mathematics, 2016, Georgia Tech
URL: http://hdl.handle.net/1853/54999
► Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis,…
(more)
▼ Fokker-Planck equations, along with
stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, both theoretically and computationally, centered around them. In part one, we consider the
optimal transport for finite discrete states, which are on a finite but arbitrary graph. By defining a discrete 2-Wasserstein metric, we derive Fokker-Planck equations on finite graphs as gradient flows of free energies. By using dynamical viewpoint, we obtain an exponential convergence result to equilibrium. This derivation provides tools for many applications, including numerics for nonlinear partial differential equations and evolutionary game theory. In part two, we introduce a new
stochastic differential equation based framework for
optimal control with constraints. The framework can efficiently solve several real world problems in differential games and Robotics, including the path-planning problem. In part three, we introduce a new noise model for
stochastic oscillators. With this model, we prove global boundedness of trajectories. In addition, we derive a pair of associated Fokker-Planck equations.
Advisors/Committee Members: Dieci, Luca (advisor), Chow, Shui Nee (committee member), Zhou, Haomin (committee member), Egerstedt, Magnus (committee member), Gangbo, Wilfrid (committee member).
Subjects/Keywords: Stochastic differential equations; Fokker-Planck equations; Gradient flow; Optimal control; Optimal transport
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APA ·
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Export
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APA (6th Edition):
Li, W. (2016). A study of stochastic differential equations and Fokker-Planck equations with applications. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/54999
Chicago Manual of Style (16th Edition):
Li, Wuchen. “A study of stochastic differential equations and Fokker-Planck equations with applications.” 2016. Doctoral Dissertation, Georgia Tech. Accessed September 15, 2019.
http://hdl.handle.net/1853/54999.
MLA Handbook (7th Edition):
Li, Wuchen. “A study of stochastic differential equations and Fokker-Planck equations with applications.” 2016. Web. 15 Sep 2019.
Vancouver:
Li W. A study of stochastic differential equations and Fokker-Planck equations with applications. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/1853/54999.
Council of Science Editors:
Li W. A study of stochastic differential equations and Fokker-Planck equations with applications. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/54999
University of California – Berkeley
15.
Miller, Christopher Wells.
Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency.
Degree: Applied Mathematics, 2016, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/56f5715d
► This thesis presents novel methods for computing optimal pre-commitment strategies in time-inconsistent optimal stochastic control and optimal stopping problems. We demonstrate how a time-inconsistent problem…
(more)
▼ This thesis presents novel methods for computing optimal pre-commitment strategies in time-inconsistent optimal stochastic control and optimal stopping problems. We demonstrate how a time-inconsistent problem can often be re-written in terms of a sequential optimization problem involving the value function of a time-consistent optimal control problem in a higher-dimensional state-space. In particular, we obtain optimal pre-commitment strategies in a non-linear optimal stopping problem, in an optimal stochastic control problem involving conditional value-at-risk, and in an optimal stopping problem with a distribution constraint on the admissible stopping times. In each case, we relate the original problem to auxiliary time-consistent problems, the value functions of which may be characterized in terms of viscosity solutions of a Hamilton-Jacobi-Bellman equation.
Subjects/Keywords: Applied mathematics; Mathematical finance; Optimal stochastic control; Optimal stopping problems; Time-inconsistency
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APA ·
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MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Miller, C. W. (2016). Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/56f5715d
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Miller, Christopher Wells. “Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency.” 2016. Thesis, University of California – Berkeley. Accessed September 15, 2019.
http://www.escholarship.org/uc/item/56f5715d.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Miller, Christopher Wells. “Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency.” 2016. Web. 15 Sep 2019.
Vancouver:
Miller CW. Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency. [Internet] [Thesis]. University of California – Berkeley; 2016. [cited 2019 Sep 15].
Available from: http://www.escholarship.org/uc/item/56f5715d.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Miller CW. Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency. [Thesis]. University of California – Berkeley; 2016. Available from: http://www.escholarship.org/uc/item/56f5715d
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Manchester
16.
Cheng, Mingliang.
CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS.
Degree: 2016, University of Manchester
URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:298233
► We investigate the impact of cash reserves upon the optimal behaviour of a modelled firm that has uncertain future revenues. To achieve this, we build…
(more)
▼ We investigate the impact of cash reserves upon the
optimal behaviour of a modelled firm that has uncertain future
revenues. To achieve this, we build up a corporate financing model
of a firm from a Real Options foundation, with the option to close
as a core business decision maintained throughout. We model the
firm by employing an
optimal stochastic control mathematical
approach, which is based upon a partial differential equations
perspective. In so doing, we are able to assess the incremental
impacts upon the
optimal operation of the cash constrained firm, by
sequentially including: an
optimal dividend distribution;
optimal
equity financing; and
optimal debt financing (conducted in a novel
equilibrium setting between firm and creditor). We present
efficient numerical schemes to solve these models, which are
generally built from the Projected Successive Over Relaxation
(PSOR) method, and the Semi-Lagrangian approach. Using these
numerical tools, and our gained economic insights, we then allow
the firm the option to also expand the operation, so they may also
take advantage of favourable economic conditions.
Advisors/Committee Members: JOHNSON, PAUL PV, Johnson, Paul, Evatt, Geoffrey.
Subjects/Keywords: Corporate Finance; Real Options; Debt Financing; Optimal Investment; Stochastic Control; Semi-Lagrangian Methods; Optimal Dividends
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APA (6th Edition):
Cheng, M. (2016). CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:298233
Chicago Manual of Style (16th Edition):
Cheng, Mingliang. “CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS.” 2016. Doctoral Dissertation, University of Manchester. Accessed September 15, 2019.
http://www.manchester.ac.uk/escholar/uk-ac-man-scw:298233.
MLA Handbook (7th Edition):
Cheng, Mingliang. “CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS.” 2016. Web. 15 Sep 2019.
Vancouver:
Cheng M. CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2019 Sep 15].
Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:298233.
Council of Science Editors:
Cheng M. CORPORATE VALUATION AND OPTIMAL OPERATION UNDER LIQUIDITY
CONSTRAINTS. [Doctoral Dissertation]. University of Manchester; 2016. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:298233
University of California – Santa Cruz
17.
Anderson, Ross.
Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models.
Degree: Applied Mathematics and Statistics, 2014, University of California – Santa Cruz
URL: http://www.escholarship.org/uc/item/3400q1w1
► Control of autonomous vehicle teams has emerged as a key topic in the control and robotics communities, owing to a growing range of applications that…
(more)
▼ Control of autonomous vehicle teams has emerged as a key topic in the control and robotics communities, owing to a growing range of applications that can benefit from the increased functionality provided by multiple vehicles. However, the mathematical analysis of the vehicle control problems is complicated by their nonholonomic and kinodynamic constraints, and, due to environmental uncertainties and information flow constraints, the vehicles operate with heightened uncertainty about the team's future motion. In this dissertation, we are motivated by autonomous vehicle control problems that highlight these uncertainties, with in particular attention paid to the uncertainty in the future motion of a secondary agent. Focusing on the Dubins vehicle and unicycle model, we propose a stochastic modeling and optimal feedback control approach that anticipates the uncertainty inherent to the systems. We first consider the application of a Dubins vehicle that should maintain a nominal distance from a target with an unknown future trajectory, such as a tagged animal or vehicle. Stochasticity is introduced in the problem by assuming that the target's motion can be modeled as a Wiener process, and the possibility for the loss of target observations is modeled using stochastic transitions between discrete states. An optimal control policy that is consistent with the stochastic kinematics is computed and is shown to perform well both in the case of a Brownian target and for natural, smooth target motion. We also characterize the resulting optimal feedback control laws in comparison to their deterministic counterparts for the case of a Dubins vehicle in a stochastically varying wind. Turning to the case of multiple vehicles, we develop a method using a Kalman smoothing algorithm for multiple vehicles to enhance an underlying analytic feedback control. The vehicles achieve a formation optimally and in a manner that is robust to uncertainty. To deal with a key implementation issue of these controllers on autonomous vehicle systems, we propose a self-triggering scheme for stochastic control systems, whereby the time points at which the control loop should be closed are computed from predictions of the process in a way that ensures stability.
Subjects/Keywords: Applied mathematics; Robotics; dubins vehicle; nonlinear control; path-integral control; self-triggered control; stochastic optimal control; stochastic processes
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
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to Zotero / EndNote / Reference
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APA (6th Edition):
Anderson, R. (2014). Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models. (Thesis). University of California – Santa Cruz. Retrieved from http://www.escholarship.org/uc/item/3400q1w1
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Anderson, Ross. “Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models.” 2014. Thesis, University of California – Santa Cruz. Accessed September 15, 2019.
http://www.escholarship.org/uc/item/3400q1w1.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Anderson, Ross. “Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models.” 2014. Web. 15 Sep 2019.
Vancouver:
Anderson R. Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models. [Internet] [Thesis]. University of California – Santa Cruz; 2014. [cited 2019 Sep 15].
Available from: http://www.escholarship.org/uc/item/3400q1w1.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Anderson R. Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models. [Thesis]. University of California – Santa Cruz; 2014. Available from: http://www.escholarship.org/uc/item/3400q1w1
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
North Carolina State University
18.
Marten, Alex Lennart.
Essays on the Application and Computation of Real Options.
Degree: PhD, Economics, 2009, North Carolina State University
URL: http://www.lib.ncsu.edu/resolver/1840.16/3725
► This dissertation presents a series of three essays that examine applications and computational issues associated with the use of stochastic optimal control modeling in the…
(more)
▼ This dissertation presents a series of three essays that examine applications and computational issues associated with the use of
stochastic optimal control modeling in the field of economics. In the first essay we examine the problem of valuing brownfield remediation and redevelopment projects amid regulatory and market uncertainty. A real options framework is developed to model the dynamic behavior of developers working with environmentally contaminated land in an investment environment with
stochastic real estate prices and an uncertain entitlement process. In a case study of an actual brownfield regeneration project we examine the impact of entitlement risk on the value of the site and
optimal developer behavior. The second essay presents a numerical method for solving
optimal switching models combined with a
stochastic control. For this class of hybrid
control problems the value function and the
optimal control policy are the solution to a Hamilton-Jacobi-Bellman quasi-variational inequality. We present a technique whereby approximating the value function using projection methods the Hamilton-Jacobi-Bellman quasi-variational inequality may be recast as extended vertical non-linear complementarity problem that may be solved using Newton's method. In the third essay we present a new method for estimating the parameters of
stochastic differential equations using low observation frequency data. The technique utilizes a quasi-maximum likelihood framework with the assumption of a Gaussian conditional transition density for the process. In order to reduce the error associated with the normality assumption sub-intervals are incorporated and integrated out using the Chapman-Kolmogorov equation and multi-dimensional Gauss Hermite quadrature. Further improvements are made through the use of Richardson extrapolation and higher order approximations for the conditional mean and variance of the process, resulting in an algorithm that may easily produce third and fourth order approximations for the conditional transition density.
Advisors/Committee Members: Roger von Haefen, Committee Member (advisor), Paul Fackler, Committee Chair (advisor), Denis Pelletier, Committee Member (advisor), John Seater, Committee Member (advisor).
Subjects/Keywords: stochastic optimal control; real options; conditional transition density; brownfields; stochastic differential equations
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APA (6th Edition):
Marten, A. L. (2009). Essays on the Application and Computation of Real Options. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/3725
Chicago Manual of Style (16th Edition):
Marten, Alex Lennart. “Essays on the Application and Computation of Real Options.” 2009. Doctoral Dissertation, North Carolina State University. Accessed September 15, 2019.
http://www.lib.ncsu.edu/resolver/1840.16/3725.
MLA Handbook (7th Edition):
Marten, Alex Lennart. “Essays on the Application and Computation of Real Options.” 2009. Web. 15 Sep 2019.
Vancouver:
Marten AL. Essays on the Application and Computation of Real Options. [Internet] [Doctoral dissertation]. North Carolina State University; 2009. [cited 2019 Sep 15].
Available from: http://www.lib.ncsu.edu/resolver/1840.16/3725.
Council of Science Editors:
Marten AL. Essays on the Application and Computation of Real Options. [Doctoral Dissertation]. North Carolina State University; 2009. Available from: http://www.lib.ncsu.edu/resolver/1840.16/3725
Penn State University
19.
Caliz Ospino, Rodrigo Alberto.
A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks.
Degree: PhD, Industrial Engineering, 2009, Penn State University
URL: https://etda.libraries.psu.edu/catalog/10319
► This research work presents a hierarchical nonlinear optimization-based framework for planning and scheduling of supply networks modeled as multi-class stochastic queueing networks. More precisely, the…
(more)
▼ This research work presents a hierarchical nonlinear
optimization-based framework for planning and scheduling of supply
networks modeled as multi-class stochastic queueing networks. More
precisely, the framework has two decision layers. At the top level
a tactical processing plan is designed. This is accomplished by
means of a nonlinear optimal control formulation, along with
suitable solution algorithms, to compute on a rolling-horizon basis
a tactical processing plan which yields the lowest cost
expected-value inventory trajectory. In doing so, raw materials,
inventory and demand mismatching costs are considered. As the main
outcome, a target inventory trajectory is obtained for each
inventory buer in the network at all times within a rolling
planning time window. The bottom layer in turn deals with a
distributed scheduling framework to best track the inventory
targets generated by the tactical processing plan. In this regard,
a processing schedule is generated for each server in the system so
that sequence-dependent and inventory holding costs are minimized
for each server within the current planning time window.
Uncertainty in the inventory accumulation and depletion processes
as well as network interrelations is accounted for by means of a
robust optimization formulation. Several numerical examples are
presented in order to illustrate the framework mechanics as well as
the algorithmic issues inherent to the different optimization steps
performed on a hierarchical basis. The planning framework can also
be adapted to standard Enterprise Resource Systems (ERPs) to best
support the planning and scheduling functions on a regular
basis.
Subjects/Keywords: Production Planning; Robust Scheduling; Multi-class
Stochastic Networks; Optimal Control
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APA ·
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Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Caliz Ospino, R. A. (2009). A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10319
Chicago Manual of Style (16th Edition):
Caliz Ospino, Rodrigo Alberto. “A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks.” 2009. Doctoral Dissertation, Penn State University. Accessed September 15, 2019.
https://etda.libraries.psu.edu/catalog/10319.
MLA Handbook (7th Edition):
Caliz Ospino, Rodrigo Alberto. “A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks.” 2009. Web. 15 Sep 2019.
Vancouver:
Caliz Ospino RA. A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks. [Internet] [Doctoral dissertation]. Penn State University; 2009. [cited 2019 Sep 15].
Available from: https://etda.libraries.psu.edu/catalog/10319.
Council of Science Editors:
Caliz Ospino RA. A Nonlinear Queueing-Based Planning and Scheduling Framework
for Multi-Product Supply Networks. [Doctoral Dissertation]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/10319
Universidade Nova
20.
Valacchi, Giulia.
An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism.
Degree: 2013, Universidade Nova
URL: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11603
► A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business…
(more)
▼ A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics
The increasing global attention to greenhouse emissions and the recent creation of EU Emission Trading Scheme has clearly suggested the need of consistent methods to value projects aimed to reduce gases. This need particularly concerns companies that have to find a way to both remain profitable and conform to new legal requirements. Multiple ways of cutting emission costs are available nowadays: short term abatement measures, which primary involve switching production machinery from coal to gas; long term abatement measures, which envisage the implementation of new types of projects .e.g Clean Development Mechanism or Joint Implementation Mechanism suggested by Kyoto Protocol -. In this work we study the impact of the introduction of both kinds of policy in a pricing model for CO2 allowances.
Advisors/Committee Members: Georgiev, Iliyan.
Subjects/Keywords: CO2 emission certificates; EU-ETS system; CDM projects; Stochastic optimal control
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Manager
APA (6th Edition):
Valacchi, G. (2013). An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism. (Thesis). Universidade Nova. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11603
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Valacchi, Giulia. “An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism.” 2013. Thesis, Universidade Nova. Accessed September 15, 2019.
http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11603.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Valacchi, Giulia. “An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism.” 2013. Web. 15 Sep 2019.
Vancouver:
Valacchi G. An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism. [Internet] [Thesis]. Universidade Nova; 2013. [cited 2019 Sep 15].
Available from: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11603.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Valacchi G. An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism. [Thesis]. Universidade Nova; 2013. Available from: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11603
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of the Western Cape
21.
Adebiyi, Ayodeji O.
Mathematical modeling of the population dynamics of tuberculosis
.
Degree: 2016, University of the Western Cape
URL: http://hdl.handle.net/11394/4928
► Tuberculosis (TB) is currently one of the major public health challenges in South Africa, and in many countries. Mycobacterium tuberculosis is among the leading causes…
(more)
▼ Tuberculosis (TB) is currently one of the major public health challenges in South Africa, and in many countries. Mycobacterium tuberculosis is among the leading causes of morbidity and mortality. It is known that tuberculosis is a curable infectious disease. In the case of incomplete treatment, however, the remains of Mycobacterium tuberculosis in the human system often results in the bacterium developing resistance to antibiotics. This leads to relapse and treatment against the resistant bacterium is extremely expensive and difficult. The aim of this work is to present and analyse mathematical models of the population dynamics of tuberculosis for the purpose of studying the effects of efficient treatment versus incomplete treatment. We analyse the spread, asymptotic behavior and possible eradication of the disease, versus persistence of tuberculosis. In particular, we
consider inflow of infectives into the population, and we study the effects of screening. A sub-model will be studied to analyse the transmission dynamics of TB in an isolated population. The full model will take care of the inflow of susceptibles as well as inflow of TB infectives into the population. This dissertation enriches the existing literature with contributions in the form of
optimal control and
stochastic perturbation. We also show how
stochastic perturbation can improve the stability of an equilibrium point. Our methods include Lyapunov functions,
optimal control and
stochastic differential equations. In the stability analysis of the DFE we show how backward bifurcation appears. Various phenomena are illustrated by way of simulations.
Advisors/Committee Members: Witbooi, Peter J (advisor).
Subjects/Keywords: Tuberculosis;
Backward bifurcation;
Stochastic asymptotic stability;
Optimal control
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Export
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Manager
APA (6th Edition):
Adebiyi, A. O. (2016). Mathematical modeling of the population dynamics of tuberculosis
. (Thesis). University of the Western Cape. Retrieved from http://hdl.handle.net/11394/4928
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Adebiyi, Ayodeji O. “Mathematical modeling of the population dynamics of tuberculosis
.” 2016. Thesis, University of the Western Cape. Accessed September 15, 2019.
http://hdl.handle.net/11394/4928.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Adebiyi, Ayodeji O. “Mathematical modeling of the population dynamics of tuberculosis
.” 2016. Web. 15 Sep 2019.
Vancouver:
Adebiyi AO. Mathematical modeling of the population dynamics of tuberculosis
. [Internet] [Thesis]. University of the Western Cape; 2016. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/11394/4928.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Adebiyi AO. Mathematical modeling of the population dynamics of tuberculosis
. [Thesis]. University of the Western Cape; 2016. Available from: http://hdl.handle.net/11394/4928
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Wayne State University
22.
Nguyen, Nhat Do Minh.
On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case.
Degree: PhD, Mathematics, 2015, Wayne State University
URL: https://digitalcommons.wayne.edu/oa_dissertations/1379
► This dissertation considers a stochastic dynamic system which is governed by a multidimensional diffusion process with time dependent coefficients. The control acts additively on…
(more)
▼ This dissertation considers a
stochastic dynamic system which is governed by a multidimensional diffusion process with time dependent coefficients. The
control acts additively on the state of the system. The objective is to minimize the expected cumulative cost associated with the position of the system and the amount of
control exerted. It is proved that Hamilton-Jacobi-Bellman’s equation of the problem has a solution, which corresponds to the
optimal cost of the problem. We also investigate the smoothness of the free boundary arising from the problem.
In the second part of the dissertation, we study the backward parabolic problem for a nonlinear parabolic equation of the form u
t + Au(t) = f (t, u(t)), u(T ) = ϕ, where A is a positive self-adjoint unbounded operator and f is a Lipschitz function. The problem is ill-posed, in the sense that if the solution does exist, it will not depend continuously on the data. To regularize the problem, we use the quasi-reversibility method to establish a modified problem. We present approximated solutions that depend on a small parameter ε > 0 and give error estimates for our regularization. These
results extend some work on the nonlinear backward problem. Some numerical examples are given to justify the theoretical analysis.
Advisors/Committee Members: Jose L. Menaldi.
Subjects/Keywords: dynamic programming; free boundary; optimal stochastic control; Mathematics
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APA (6th Edition):
Nguyen, N. D. M. (2015). On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case. (Doctoral Dissertation). Wayne State University. Retrieved from https://digitalcommons.wayne.edu/oa_dissertations/1379
Chicago Manual of Style (16th Edition):
Nguyen, Nhat Do Minh. “On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case.” 2015. Doctoral Dissertation, Wayne State University. Accessed September 15, 2019.
https://digitalcommons.wayne.edu/oa_dissertations/1379.
MLA Handbook (7th Edition):
Nguyen, Nhat Do Minh. “On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case.” 2015. Web. 15 Sep 2019.
Vancouver:
Nguyen NDM. On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case. [Internet] [Doctoral dissertation]. Wayne State University; 2015. [cited 2019 Sep 15].
Available from: https://digitalcommons.wayne.edu/oa_dissertations/1379.
Council of Science Editors:
Nguyen NDM. On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case. [Doctoral Dissertation]. Wayne State University; 2015. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1379
University of Toronto
23.
Rubisov, Anton.
Statistical Arbitrage Using Limit Order Book Imbalance.
Degree: 2015, University of Toronto
URL: http://hdl.handle.net/1807/70567
► This dissertation demonstrates that there is high revenue potential in using limit order book imbalance as a state variable in an algorithmic trading strategy. Beginning…
(more)
▼ This dissertation demonstrates that there is high revenue potential in using limit order book imbalance as a state variable in an algorithmic trading strategy. Beginning with the hypothesis that imbalance of bid/ask order volumes is an indicator for future price changes, exploratory data analysis suggests that modelling the joint distribution of imbalance and observed price changes as a continuous-time Markov chain presents a monetizable opportunity. The arbitrage problem is then formalized mathematically as a stochastic optimal control problem using limit orders and market orders with the aim of maximizing terminal wealth. The problem is solved in both continuous and discrete time using the dynamic programming principle, which produces both conditions for market order execution, as well as limit order posting depths, as functions of time, inventory, and imbalance. The optimal controls are calibrated and backtested on historical NASDAQ ITCH data, which produces consistent and substantial revenue.
M.A.S.
Advisors/Committee Members: D'Eleuterio, Gabriele M.T., Jaimungal, Sebastian, Aerospace Science and Engineering.
Subjects/Keywords: dynamic programming; limit order book; statistical arbitrage; stochastic optimal control; 0508
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Manager
APA (6th Edition):
Rubisov, A. (2015). Statistical Arbitrage Using Limit Order Book Imbalance. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/70567
Chicago Manual of Style (16th Edition):
Rubisov, Anton. “Statistical Arbitrage Using Limit Order Book Imbalance.” 2015. Masters Thesis, University of Toronto. Accessed September 15, 2019.
http://hdl.handle.net/1807/70567.
MLA Handbook (7th Edition):
Rubisov, Anton. “Statistical Arbitrage Using Limit Order Book Imbalance.” 2015. Web. 15 Sep 2019.
Vancouver:
Rubisov A. Statistical Arbitrage Using Limit Order Book Imbalance. [Internet] [Masters thesis]. University of Toronto; 2015. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/1807/70567.
Council of Science Editors:
Rubisov A. Statistical Arbitrage Using Limit Order Book Imbalance. [Masters Thesis]. University of Toronto; 2015. Available from: http://hdl.handle.net/1807/70567
Technical University of Lisbon
24.
Barros, Gilson Lopes Barbosa.
Problemas de consumo e investimento em mercados financeiros.
Degree: 2014, Technical University of Lisbon
URL: http://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/7413
► Mestrado em Matemática Financeira
Um agente económico pretende decidir de que forma alocar a sua riqueza no que diz respeito ao seu nível de consumo…
(more)
▼ Mestrado em Matemática Financeira
Um agente económico pretende decidir de que forma alocar a sua riqueza no que diz respeito ao seu nível de consumo e ao investimento num mercado financeiro subjacente de forma a maximizar a sua utilidade esperada, derivada do consumo instantâneo ao longo de um dado intervalo de tempo e da sua riqueza no instante final desse intervalo. Assumimos que o mercado financeiro é composto por um activo sem risco e um activo com risco, com a particularidade da evolução temporal do activo com risco ser dada por uma equação diferencial estocástica com coeficientes com reversão à média. Este é um problema de controlo óptimo estocástico, que vai ser estudado com recurso a técnicas de programação dinâmica. O objectivo final deste trabalho é determinar as estratégias de consumo e investimento óptimas e compará-las com as estratégias clássicas do problema de consumo e investimento de Merton.
An economic agent is faced with the problem of deciding how to allocate her wealth among consumption and investment in an underlying financial market, in order to maximize the expected utility derived from the instantaneous consumption over a given time interval and her wealth at the final horizon. We assume that the financial market under consideration consists of a riskless asset and a risky asset, the latter having the special feature that its temporal evolution is given by a stochastic differential equation with mean reversion coefficients. Dynamic programming techniques will be employed to solve this Stochastic Optimal Control problem with the goal of finding the optimal strategies for consumption and investment and compare it with Merton's optimal strategies.
Advisors/Committee Members: Pinheiro, Diogo Araújo.
Subjects/Keywords: Controlo óptimo estocástico; consumo-investimento óptimo; programação dinâmica; volatilidade estocástica; Stochastic optimal control; optimal consumption-investment; dynamic programming; stochastic volatility
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Barros, G. L. B. (2014). Problemas de consumo e investimento em mercados financeiros. (Thesis). Technical University of Lisbon. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/7413
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Barros, Gilson Lopes Barbosa. “Problemas de consumo e investimento em mercados financeiros.” 2014. Thesis, Technical University of Lisbon. Accessed September 15, 2019.
http://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/7413.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Barros, Gilson Lopes Barbosa. “Problemas de consumo e investimento em mercados financeiros.” 2014. Web. 15 Sep 2019.
Vancouver:
Barros GLB. Problemas de consumo e investimento em mercados financeiros. [Internet] [Thesis]. Technical University of Lisbon; 2014. [cited 2019 Sep 15].
Available from: http://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/7413.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Barros GLB. Problemas de consumo e investimento em mercados financeiros. [Thesis]. Technical University of Lisbon; 2014. Available from: http://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/7413
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Oxford
25.
Fleming, James.
Robust and stochastic MPC of uncertain-parameter systems.
Degree: PhD, 2016, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730224
► Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with…
(more)
▼ Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of âsample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.
Subjects/Keywords: 629.8; Convex Optimization; Stochastic Control; Chance Constrained Programming; Robust Control; Model Predictive Control; Optimal Control; Control; Receding-horizon; Optimal; Convex; Robust; Stochastic; Optimisation; MPC; Tube MPC; Constraints
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APA (6th Edition):
Fleming, J. (2016). Robust and stochastic MPC of uncertain-parameter systems. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730224
Chicago Manual of Style (16th Edition):
Fleming, James. “Robust and stochastic MPC of uncertain-parameter systems.” 2016. Doctoral Dissertation, University of Oxford. Accessed September 15, 2019.
https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730224.
MLA Handbook (7th Edition):
Fleming, James. “Robust and stochastic MPC of uncertain-parameter systems.” 2016. Web. 15 Sep 2019.
Vancouver:
Fleming J. Robust and stochastic MPC of uncertain-parameter systems. [Internet] [Doctoral dissertation]. University of Oxford; 2016. [cited 2019 Sep 15].
Available from: https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730224.
Council of Science Editors:
Fleming J. Robust and stochastic MPC of uncertain-parameter systems. [Doctoral Dissertation]. University of Oxford; 2016. Available from: https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730224
26.
Li, Liangchen.
Stochastic nonzero-sum duopoly games with economic applications.
Degree: 2019, University of California – eScholarship, University of California
URL: http://www.escholarship.org/uc/item/28x554n4
► We study a class of stochastic duopoly games inspired by the two time-scale feature of many markets. The firms convert their short-term “local” advantage driven…
(more)
▼ We study a class of stochastic duopoly games inspired by the two time-scale feature of many markets. The firms convert their short-term “local” advantage driven by exogenous infinitesimal shocks into a more durable gain through long-term market dominance. As an extension of existing literature, we consider two asymmetric players each of whom adopts timing strategies to increase her profitability and possibly bring negative externality to the rival. In turn, this leads us to more general settings of nonzero-sum games. Characterizing Nash equilibrium as a fixed-point of each player’s best-response to her rival, we construct threshold-type Feedback Nash Equilibrium via best response iteration. Our main contribution is explicitly constructing equilibria for types of duopoly games that represent a wide range of industries. Motivated by the competition among sectors of power generators, we consider a duopoly of producers with finite options to increase their production capacity. We study nonzero-sum games in which two players compete for market dominance via switching controls. We also study mixed switching and impulses games inspired by the vertical competition among the producers and consumers of a commodity. Our analysis quantifies the dynamic competition effects and brings economic insights.
Subjects/Keywords: Applied mathematics; Operations research; Economics; dynamic duopoly; nonzero-sum stochastic game; optimal stochastic control; optimal stopping; special type of equilibria; stochastic impulse control
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APA ·
Chicago ·
MLA ·
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APA (6th Edition):
Li, L. (2019). Stochastic nonzero-sum duopoly games with economic applications. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/28x554n4
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Li, Liangchen. “Stochastic nonzero-sum duopoly games with economic applications.” 2019. Thesis, University of California – eScholarship, University of California. Accessed September 15, 2019.
http://www.escholarship.org/uc/item/28x554n4.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Li, Liangchen. “Stochastic nonzero-sum duopoly games with economic applications.” 2019. Web. 15 Sep 2019.
Vancouver:
Li L. Stochastic nonzero-sum duopoly games with economic applications. [Internet] [Thesis]. University of California – eScholarship, University of California; 2019. [cited 2019 Sep 15].
Available from: http://www.escholarship.org/uc/item/28x554n4.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Li L. Stochastic nonzero-sum duopoly games with economic applications. [Thesis]. University of California – eScholarship, University of California; 2019. Available from: http://www.escholarship.org/uc/item/28x554n4
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Illinois – Urbana-Champaign
27.
Golpashin, Alen Envieh.
Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control.
Degree: MS, Aerospace Engineering, 2018, University of Illinois – Urbana-Champaign
URL: http://hdl.handle.net/2142/102525
► This study aims to address the problem of attitude control of spacecraft in presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with…
(more)
▼ This study aims to address the problem of attitude
control of spacecraft in presence of thrust uncertainty, which leads to
stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These
stochastic processes arise from sources such as uncertain power supply output, varying propellant flow rate, faulty thrusters, etc. Mission requirements and mass/fuel limitations demand an
optimal and proactive method of
control to mitigate the thrust uncertainty and parasitic torque. Stabilizing
stochastic optimal control of the satellite attitude dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a
stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a
stochastic system was first presented in [2]; detailed derivations of linear and nonlinear
stochastic control laws along with their analytical and numerical analyses are presented in this thesis. A planning method is then discussed to lower the error due to local nature of the
control.
Advisors/Committee Members: Namachchivaya, Navaratnam S. (advisor), Ho, Koki (advisor).
Subjects/Keywords: Stochastic Optimal Control; Attitude Control; Thrust Uncertainty; Hamilton-Jacobi-Bellman; HJB; Al'brekht Method
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APA ·
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MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Golpashin, A. E. (2018). Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/102525
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Golpashin, Alen Envieh. “Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control.” 2018. Thesis, University of Illinois – Urbana-Champaign. Accessed September 15, 2019.
http://hdl.handle.net/2142/102525.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Golpashin, Alen Envieh. “Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control.” 2018. Web. 15 Sep 2019.
Vancouver:
Golpashin AE. Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Sep 15].
Available from: http://hdl.handle.net/2142/102525.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Golpashin AE. Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control. [Thesis]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/102525
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
28.
Riquelme, Victor.
Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau.
Degree: Docteur es, Mathématiques et modélisation, 2016, Montpellier; Universidad de Chile
URL: http://www.theses.fr/2016MONTT290
► Cette thèse se compose de deux parties. Dans la première partie, nous étudions les stratégies de temps minimum pour le traitement de la pollution dans…
(more)
▼ Cette thèse se compose de deux parties. Dans la première partie, nous étudions les stratégies de temps minimum pour le traitement de la pollution dans de grandes ressources en eau, par exemple des lacs ou réservoirs naturels, à l'aide d'un bioréacteur continu qui fonctionne à un état quasi stationnaire. On contrôle le débit d'entrée d'eau au bioréacteur, dont la sortie revient à la ressource avec le même débit. Nous disposons de l'hypothèse d'homogénéité de la concentration de polluant dans la ressource en proposant trois modèles spatialement structurés. Le premier modèle considère deux zones connectées l'une à l'autre par diffusion et seulement une d'entre elles connectée au bioréacteur. Avec l'aide du Principe du Maximum de Pontryagin, nous montrons que le contrôle
optimal en boucle fermée dépend seulement des mesures de pollution dans la zone traitée, sans influence des paramètres de volume, diffusion, ou la concentration dans la zone non traitée. Nous montrons que l'effet d'une pompe de recirculation qui aide à homogénéiser les deux zones est avantageux si opérée à vitesse maximale. Nous prouvons que la famille de fonctions de temps minimal en fonction du paramètre de diffusion est décroissante. Le deuxième modèle consiste en deux zones connectées l'une à l'autre par diffusion et les deux connectées au bioréacteur. Ceci est un problème dont l'ensemble des vitesses est non convexe, pour lequel il n'est pas possible de prouver directement l'existence des solutions. Nous surmontons cette difficulté et résolvons entièrement le problème étudié en appliquant le principe de Pontryagin au problème de contrôle relaxé associé, obtenant un contrôle en boucle fermée qui traite la zone la plus polluée jusqu'au l'homogénéisation des deux concentrations. Nous obtenons des limites explicites sur la fonction valeur via des techniques de Hamilton-Jacobi-Bellman. Nous prouvons que la fonction de temps minimal est non monotone par rapport au paramètre de diffusion. Le troisième modèle consiste en deux zones connectées au bioréacteur en série et une pompe de recirculation entre elles. L'ensemble des contrôles dépend de l'état, et nous montrons que la contrainte est active à partir d'un temps jusqu'à la fin du processus. Nous montrons que le contrôle
optimal consiste à l'atteinte d'un temps à partir duquel il est
optimal de recirculer à vitesse maximale et ensuite ré-polluer la deuxième zone avec la concentration de la première. Ce résultat est non intuitif. Des simulations numériques illustrent les résultats théoriques, et les stratégies optimales obtenues sont testées sur des modèles hydrodynamiques, en montrant qu'elles sont de bonnes approximations de la solution du problème inhomogène. La deuxième partie consiste au développement et l'étude d'un modèle stochastique de réacteur biologique séquentiel. Le modèle est obtenu comme une limite des processus de naissance et de mort. Nous établissons l'existence et l'unicité des solutions de l'équation contrôlée qui ne satisfait pas les hypothèses habituelles. Nous prouvons que pour…
Advisors/Committee Members: Rapaport, Alain (thesis director), Ramirez, Hector (thesis director).
Subjects/Keywords: Contrôle optimal; Temps minimal; Contrôle stochastique; Biorestauration; Chemostat; Traitement de l'eau; Optimal control; Minimum time; Stochastic control; Bioremediation; Chemostat; Water treatment
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Riquelme, V. (2016). Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau. (Doctoral Dissertation). Montpellier; Universidad de Chile. Retrieved from http://www.theses.fr/2016MONTT290
Chicago Manual of Style (16th Edition):
Riquelme, Victor. “Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau.” 2016. Doctoral Dissertation, Montpellier; Universidad de Chile. Accessed September 15, 2019.
http://www.theses.fr/2016MONTT290.
MLA Handbook (7th Edition):
Riquelme, Victor. “Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau.” 2016. Web. 15 Sep 2019.
Vancouver:
Riquelme V. Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau. [Internet] [Doctoral dissertation]. Montpellier; Universidad de Chile; 2016. [cited 2019 Sep 15].
Available from: http://www.theses.fr/2016MONTT290.
Council of Science Editors:
Riquelme V. Optimal control problems for bioremediation of water resources : Problèmes de contrôle optimal pour la bioremédiation de ressources en eau. [Doctoral Dissertation]. Montpellier; Universidad de Chile; 2016. Available from: http://www.theses.fr/2016MONTT290
Indian Institute of Science
29.
Saha, Subhamay.
Single and Multi-player Stochastic Dynamic Optimization.
Degree: 2013, Indian Institute of Science
URL: http://etd.iisc.ernet.in/2005/3357
;
http://etd.iisc.ernet.in/abstracts/4224/G25755-Abs.pdf
► In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we…
(more)
▼ In this thesis we investigate single and multi-player
stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both complete and partial information. We study partially observable
stochastic games with average cost criterion and the state process be-ing discrete time controlled Markov chain. The idea involved in studying this problem is to replace the original unobservable state variable with a suitable completely observable state variable. We establish the existence of the value of the game and also obtain
optimal strategies for both players. We also study a continuous time zero-sum
stochastic game with complete observation. In this case the state is a pure jump Markov process. We investigate the nite horizon total cost criterion. We characterise the value function via appropriate Isaacs equations. This also yields
optimal Markov strategies for both players.
In the single player setup we investigate risk-sensitive
control of continuous time Markov chains. We consider both nite and in nite horizon problems. For the nite horizon total cost problem and the in nite horizon discounted cost problem we characterise the value function as the unique solution of appropriate Hamilton Jacobi Bellman equations. We also derive
optimal Markov controls in both the cases. For the in nite horizon average cost case we shown the existence of an
optimal stationary
control. we also give a value iteration scheme for computing the
optimal control in the case of nite state and action spaces.
Further we introduce a new class of
stochastic processes which we call
stochastic processes with \age-dependent transition rates". We give a rigorous construction of the process. We prove that under certain assunptions the process is Feller. We also compute the limiting probabilities for our process. We then study the controlled version of the above process. In this case we take the risk-neutral cost criterion. We solve the in nite horizon discounted cost problem and the average cost problem for this process. The crucial step in analysing these problems is to prove that the original
control problem is equivalent to an appropriate semi-Markov decision problem. Then the value functions and
optimal controls are characterised using this equivalence and the theory of semi-Markov decision processes (SMDP). The analysis of nite horizon problems becomes di erent from that of in nite horizon problems because of the fact that in this case the idea of converting into an equivalent SMDP does not seem to work. So we deal with the nite horizon total cost problem by showing that our problem is equivalent to another appropriately de ned discrete time Markov decision problem. This allows us to characterise the value function and to nd an
optimal Markov
control.
Advisors/Committee Members: Ghosh, Mrinal Kanti.
Subjects/Keywords: Stochastic Dynamic Optimization; Stochastic Control Theory; Stochastic Processes; Markov Processes; Continuous-Time Markov Chains; Stochastic Games; Semi-Markov Decision Processes; Markov Processes - Optimal Control; Continuous Time Stochastic Processes; Dicrete Time Stochastic Processes; Continuous Time Markov Chains; Semi-Markov Decision Processes (SMDP); Optimal Markov Control; Mathematics
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Saha, S. (2013). Single and Multi-player Stochastic Dynamic Optimization. (Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ernet.in/2005/3357 ; http://etd.iisc.ernet.in/abstracts/4224/G25755-Abs.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Saha, Subhamay. “Single and Multi-player Stochastic Dynamic Optimization.” 2013. Thesis, Indian Institute of Science. Accessed September 15, 2019.
http://etd.iisc.ernet.in/2005/3357 ; http://etd.iisc.ernet.in/abstracts/4224/G25755-Abs.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Saha, Subhamay. “Single and Multi-player Stochastic Dynamic Optimization.” 2013. Web. 15 Sep 2019.
Vancouver:
Saha S. Single and Multi-player Stochastic Dynamic Optimization. [Internet] [Thesis]. Indian Institute of Science; 2013. [cited 2019 Sep 15].
Available from: http://etd.iisc.ernet.in/2005/3357 ; http://etd.iisc.ernet.in/abstracts/4224/G25755-Abs.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Saha S. Single and Multi-player Stochastic Dynamic Optimization. [Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ernet.in/2005/3357 ; http://etd.iisc.ernet.in/abstracts/4224/G25755-Abs.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
The Ohio State University
30.
El Khoury, Omar, Mr.
Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity.
Degree: PhD, Civil Engineering, 2017, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1492691287286787
► Natural disasters are one of the constant challenges for designing new and strengthening existing infrastructures. Such hazards in the past have incurred significant loss of…
(more)
▼ Natural disasters are one of the constant challenges
for designing new and strengthening existing infrastructures. Such
hazards in the past have incurred significant loss of life and
economic damage; therefore, further research is warranted in this
area to enhance the health and minimize the cost of maintaining and
upgrading infrastructures, improve residents’ comfort, and enable
achieving higher levels of life safety. To this end, the field of
hazard mitigation and
control focuses on performance improvement,
safety, and cost effectiveness of structures mostly through
minimizing large deformations of seismic-excited structures and
suppressing the damage and collapse in dynamic systems due to
excessive vibrations. Past developments in active and semi-active
control designs, such as the commonly used state space controllers
(e.g. linear quadratic regulator for fully observed systems and
linear quadratic Gaussian for partially observed systems), consider
linear feedback strategies. Meanwhile, such
control strategies
require linearization, and the system is usually linearized based
on linear elastic properties. The
control force is proportional to
the state space vector and the dynamics and constraints of
control
devices are mainly ignored. The objective functions have
restrictive forms, and are solely dependent on a second order
convex function of the response variables. To overcome the
aforementioned shortcomings, this dissertation develops new
stochastic control algorithms for active and semi-active
control
strategies. This research concentrates on the development of
frameworks that incorporate nonlinearity of the system, uncertainty
of the excitation, and constraints and dynamics of the
control
device.
Control designs are developed based on different objective
functions such as higher order polynomials of response variables,
reliability of the structure, and life cycle cost of the system
considering hazard risks in seismic prone areas. In particular, a
nonlinear sliding mode
control algorithm based on
stochastic
linearization is developed; this method supports higher order
objective functions and therefore enhances the ability of designers
to achieve design objectives. The proposed
control algorithm is
designed, optimized, and tested on a seismically excited multi-span
bridge equipped with semi-active magnetorheological dampers. Next,
a
stochastic control algorithm is presented based on a proposed
stochastic averaging method called enhanced
stochastic averaging.
This method conserves the nonlinear behavior of the system and the
stochastic nature of the excitation in
optimal control design. In
order to directly minimize the probability of failures, the
stochastic control algorithm is extended to a reliability-based
control algorithm. These
control algorithms are implemented in a
system with nonlinear soil-structure interactions. Furthermore, a
risk-based
control methodology is developed to minimize life cycle
cost of a nonlinear multi-story building subjected to seismic
excitations. The findings of these proposed…
Advisors/Committee Members: Shafieezadeh, Abdollah (Advisor).
Subjects/Keywords: Civil Engineering; Stochasticity, Nonlinearity, Seismic Excitation, Optimal
Control, Sliding Mode Control, Nonlinear Stochastic Control,
Enhanced Stochastic Averaging, Shaking Table Tests, Stochastic
Simulations, Multi-Span Bridges, Multi-Story Buildings
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
El Khoury, Omar, M. (2017). Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1492691287286787
Chicago Manual of Style (16th Edition):
El Khoury, Omar, Mr. “Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity.” 2017. Doctoral Dissertation, The Ohio State University. Accessed September 15, 2019.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1492691287286787.
MLA Handbook (7th Edition):
El Khoury, Omar, Mr. “Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity.” 2017. Web. 15 Sep 2019.
Vancouver:
El Khoury, Omar M. Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity. [Internet] [Doctoral dissertation]. The Ohio State University; 2017. [cited 2019 Sep 15].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1492691287286787.
Council of Science Editors:
El Khoury, Omar M. Optimal Performance-Based Control of Structures against
Earthquakes Considering Excitation Stochasticity and System
Nonlinearity. [Doctoral Dissertation]. The Ohio State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1492691287286787
◁ [1] [2] [3] [4] [5] ▶
. 
Open Access Theses and Dissertations