▼ This thesis considers the design of distributed state and output feedback control algorithms for linear multi-agent systems with performance guarantees in the presence of delays. The multi-agent systems considered are assumed to exchange relative information over an information network. As a first contribution, a novel distributed state feedback control design method with a sub-optimal LQR performance is developed for a network of multiple agents. For the control design process, it is assumed that the exchange of relative information is instantaneous. A stability analysis of the proposed control law is performed by incorporating delays in relative information to ascertain the maximum possible delay that can be accommodated by the communication network. Subsequently, the assumption of the exchange of instantaneous relative information in the control design process is relaxed and the relative information is assumed to be delayed. The system is then represented as a time-delay system. Distributed state feedback control synthesis methods are then developed for the system with a certain level of LQR performance. In the above contributions, the time delay analysis and the development of delay based control methods, it is implicitly assumed that delays are detrimental to achieving cooperative tasks for a multi-agent system. Subsequently, positive effects of delays in communication of relative information are explored. For this a network of vehicles described by double integrator dynamics, which cannot be stabilized by static output feedback without delays, is considered. A novel control design method to achieve exponential stabilization of such a multi-agent system by static output feedback using delayed relative information is developed. Conclusions are drawn from the results of the research presented in this thesis and a few directions for future work are identified.

▼ This dissertation presents a series of studies on the analysis and control of time-delayed dynamical systems. We first review the discrete methods of semidiscretization and digital control approach. Then we introduce a new method of continuous time approximation (CTA) for the response of linear and nonlinear dynamical systems with time delay. We investigate the accuracy of temporal responses as well as the spectral properties of the CTA method, and present several variants of the CTA method with improved accuracy. Finally, we apply the CTA method to control problems of time-delayed systems including optimal control, supervisory control and sliding mode control of uncertain systems. The CTA method creates a set of state equations for the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. The resulting state equations are in the standard state space form, making all the existing solution methods and control design tools for linear and nonlinear dynamical systems amenable to time-delayed systems. The CTA method can handle multiple independent time delays in a natural way. The work in this dissertation indicates that the CTA method is a promising method for analysis and control design of complex nonlinear time-delayed dynamical systems.

▼ In this thesis one of the recently developed gain scheduling control methods, the linear parameter varying (LPV) technique is demonstrated. Starting from the basic definitions of an LMI, important derivations of time delayed control design conditions are derived. In subsequent steps, a motivating example is shown such that the stability and performance of the system is guaranteed in the full operating envelope. The thesis consists of methods and derivations to address time-delayed LPV plants. The synthesis conditions show that the proposed controllers are not only capable of compensating the delay bound but also its rate variation bound. A main benefit of the obtained controllers is that the scheduling of the parameters lead to a robust behavior even for large delay variation and rate. Numerical examples are used to compare the past methods and the current results on the analysis and control design of the same system. Finally the internal combustion engine air-fuel ratio problem is investigated with the help of the derived output-feedback controller design results. The same problem is addressed with a Smith Predictor based Internal Model Control technique to satisfy desired transient and steady-state response characteristics. The LPV control shows better performance compared to the IMC method for small values of the delay. Simulations are used to evaluate the results for larger values of the delay. For large values of the delay the bounds on the Lyapunov –Krasovskii approach introduce some conservatism in the control design and thus, performance specifications are compromised. Advisors/Committee Members: Grigoriadis, Karolos M. (advisor), Franchek, Matthew A. (committee member), Provence, Robert S. (committee member).

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Esta tese versa sobre a síntese de compensadores antiwindup para sistemas lineares contínuos invariantes no tempo, com restrições no atuador e atraso no tempo. Baseados em um funcional Liapunov-Krasovskii e uma condição de setor para a função zona-morta já existentes na literatura, são propostas condições suficientes expressas em LMIs para a existência de compensadores antiwindup para duas classes de sistemas: sistemas com atraso nos estados, e sistemas com atraso na entrada. Em ambos os casos, considera-se a síntese de um compensador de ordem plena para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores antiwindup considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, e um conjunto de inicialização dos estados do sistema tolerante à perturbação com norma L2 inferior a um máximo, determinado juntamente com a síntese do compensador antiwindup. Na ausência de perturbação a origem é garantida assintoticamente estável. Para sistemas com atraso no estado, primeiro propõe-se um método para a síntese de compensadores dinâmicos racionais de ordem plena. Este método é baseado no Lema de Projeção. Em seguida, estende-se o resultado, propondo-se um framework genérico que permite a síntese de compensadores racionais e não racionais. Este método é baseado em uma transformação de variáveis linearizante. Para sistemas com atraso na entrada, propõe-se três resultados de síntese de compensadores antiwindup: compensadores estáticos, dinâmicos racionais, e dinâmicos não racionais. Estes métodos são novamente baseados no Lema de Projeção. Em todos os casos, as condições obtidas que garantem a existência de um compensador antiwindup são expressas em forma de LMIs e garantem a estabilidade local da origem. Em seguida, estende-se os resultados para garantir a estabilidade global da origem, nos casos em que a planta é estável em malha aberta. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída regulada. Exemplos numéricos ilustram cada método na solução dos problemas de máxima tolerância à perturbação, e minimização do ganho L2 da perturbação à saída regulada.

This thesis verses about antiwindup compensator synthesis for linear time invariant continuous systems, presenting constraints in actuator and time delay. Based on a Liapunov-Krasovskii functional and a sector condition for the dead-zone nonlinearity already castign in literature, it is proposed sufficient conditions expressed in LMI to the existance of an antiwindup compensator for two classes of systems: systems with state delay, and systems with input delay. In both cases it is considered the synthesis of a full order antiwindup compensator for a system with a controller a priori given that disregards the actuator bounds. The synthesis of antiwindup compensators considers an actuator…

Advisors/Committee Members: Silva Junior, Joao Manoel Gomes da.

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Το ερευνητικό αντικείμενο της Διατριβής είναι τα θέματα σθεναρότητας του προκύπτουν στα Δικτυωμένα Συστήματα Ελέγχου (Νetworked Cοntrοlled Systems - εφεξής "ΝCS"), όπου η βασική πηγή αβεβαιότητας είναι οι καθυστερήσεις λόγω δικτύου. Στο πλαίσιο αυτό παρουσιάζονται απότελέσματα του αφορούν στην ανάλυση σθεναρής ευστάθειας και στην σύνθεση σθεναρών ελεγκτών. Να επισημανθεί ότι στην Διατριβή, ο προσδιορισμός "σθεναρός" αφορά απόκλειστικά σθεναρότητα (ευστάθειας και επιδόσεων) ως προς τις αβέβαιες, χρονικά μεταβαλλόμενες, φραγμένες καθυστερήσεις. Τα μελετώμενα ΝCS απαρτίζονται από την διασύνδεση γραμμικών χρονικά αμετάβλητων συστημάτων συνεχούς χρόνου με ελεγκτές διακριτού χρόνου. Η βασική διάρθρωση των συστημάτων αυτών απαρτίζεται από έναν "οδηγούμενο από χρόνο" (time driven) αισθητήρα / δειγματολήπτη (με σταθερή περίοδο δειγματοληψίας h) που μεταδίδει μέσω του δικτύου τα δείγματα που λαμβάνει από το σύστημα στον "οδηγούμενο από γεγονότα" (event–driven) ελεγκτή. Ακολούθως ο ελεγκτής υπολογίζει την δράση ελέγχου και την μεταδίδει μέσω του δικτύου στον "οδηγούμενο από γεγονότα" (eveτιt–driven) ενεργοποιητή. Οι διαδικασίες της μοντελοποίησης, της ανάλυσης ευστάθειας και της σύνθεσης σθεναρών ελεγκτών (στατικών αλλά και κατά τμήματα γραμμικών) στην εργασία αυτή λαμβάνουν χώρα στο πεδίο του διακριτού χρόνου μετά από διακριτοποίηση του συνολικού συστήματος. Όσον αφορά στην ανάλυση σθεναρής ευστάθειας προτείνονται δύο προσεγγίσεις: • η πρώτη, βασιζόμενη σε ανάλυση ιδιαζουσών τιμών, είναι υπολογιστικά ελκυστική αλλά συνήθως δίδει συντηρητικά αποτελέσματα, • ενώ η δεύτερη, διατυπωμένη σαν ανισότητα πινάκων (LMI), είναι απαιτητική ως προς τον χρόνο υπολογισμού αλλά δίδει αποτελέσματα με μειωμένο συντηρητισμό. Όσον αφορά στην σύνθεση σθεναρών ελεγκτών ανατροφοδότησης κατάστασης μελετώνται οι εξής προσεγγίσεις: • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης "εγγυημένου κόστους" που απαντάει στην συνδυασμένη απαίτηση ευστάθειας και επίδοσης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Cοnstrained Controller) για ΝCS με "μικρή καθυστέρηση". Επέκταση των αποτελεσμάτων για ΝCS με "μεγάλη καθυστέρηση". Εφαρμογή των παραπάνω αποτελεσμάτων σε προβλήματα παρακολούθησης σταθερής εντολής (set point tracking). • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Constrained Controller), για ΝCS με μικρή και διακοπτική καθυστέρηση.

This research work is concerned with robustness issues arising in Νetworked Cοntrοlled Systems - ("ΝCS"), where the main sources of uncertainty are the time-varying network-induced delays. In this framework the presented results concern robust stability analysis and synthesis of robust controllers. The NCS studied consist of a Linear Time Invariant continuous time plant and a discrete time controller. This configuration includes a time driven (periodic) sampler (taking samples from the sensors with constant sampling period h) and…

Advisors/Committee Members: Τζες, Αντώνιος, Dritsas, Leonidas, Αλεξανδρίδης, Αντώνιος, Καζάκος, Δημοσθένης, Κούσουλας, Νικόλαος, Μπιτσώρης, Γεώργιος, Τζες, Αντώνιος, Φασόης, Σπήλιος.

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Cette thèse concerne la stabilisation exponentielle de systèmes commandés en réseaux (NCS en anglais) par retour de sortie. Les solutions proposées reposent sur un observateur distant et capable d’estimer l’état présent du processus malgré les différents retards générés par la présence du réseau. Le premier chapitre présente le contexte général des NCS et décrit plus particulièrement le problème étudié. Le chapitre suivant propose une architecture informatique permettant de réaliser un retour d’état distant basé sur une structure d’observateur. Deux autres chapitres proposent ensuite la synthèse d’un couple loi de commande / observateur garantissant des performances de convergence exponentielle. Les conditions correspondantes s’écrivent sous forme d’inégalités matricielles linéaires (LMI en anglais) et permettent donc une optimisation. Ces conditions sont basées sur la méthode des fonctionnelles de Lyapunov-Krasovskii et des résultats originaux sont proposés. Une première synthèse peut être effectuée globalement, une seconde permet d’adapter les performances dynamiques à la qualité de service disponible à chaque instant. La seconde approche fait intervenir des résultats originaux sur les systèmes à retards et à commutations. Dans un dernier chapitre, nous proposons une solution complètement asynchrone (gérée par événements). Dans ce cas, le problème des pertes de paquets devient crucial et nous y apportant une réponse. L’ensemble des résultats est confirmé par des expérimentations mises au point dans le cadre de ce travail, et correspondant à un robot léger commandé en temps réel à 40km de distance par Internet

This PhD thesis is dedicated to the exponential output stabilization of linear NCS (Networked Control Systems). The studied solution is based on a remote observer which is able to estimate the present state of the plant despite the various network induced delays. These last are present in both the control and the measurement channels.The first chapter describes the problem and gives a survey on the NCS. The next chapter proposes a computer structure which realizes the remote, observer-based, state feedback controller. The following two chapters propose LMI conditions (Linear Matrix Inequalities) for the design of the observer-based remote controller. The second method of Lyapunov is used with the most up-to-date Lyapunov-Krasovskii functionals. The main objective of the design is to guarantee some performances expressed in the form of exponential stability. Then some enhancements of the control strategy are given. It consists in taking into account the Quality of Service (QoS) in the controller to get better guaranteed performances. The last contribution of this work is to consider the overall system as an event-driven system. It allows one to consider packet dropout problems in the network.The effectiveness of all presented results is demonstrated by real experiments implemented on a light robot controlled over the Internet

Advisors/Committee Members: Richard, Jean-Pierre (thesis director), Toguyeni, Abdoul Karim Armand (thesis director).

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This research work is concerned with robustness issues arising in Νetworked Cοntrοlled Systems - ("ΝCS"), where the main sources of uncertainty are the time-varying network-induced delays. In this framework the presented results concern robust stability analysis and synthesis of robust controllers. The NCS studied consist of a Linear Time Invariant continuous time plant and a discrete time controller. This configuration includes a time driven (periodic) sampler (taking samples from the sensors with constant sampling period h) and an event–driven controller which transmits the control command via the network to the event–driven actuator. Two modeling approaches for Networked Controlled Systems (NCS) with uncertainly varying bounded transmission delays and static discrete – time control laws are presented. Different models are offered for each case, all linked to the objective of designing robust discrete-time controllers. It is shown how the careful mixing of asynchronous (event – driven) and synchronized (clocked) signals can lead to discrete time uncertain (possibly switched) systems. Two families of sufficient conditions for robust stability are given for each approach and a comparison of the conservation of results is discussed. The first group of robust stability results (one for each of the two discrete-time NCS models) is based on a singular value formulation, which although conservative, is extremely simple and has low computational cost. The second one is derived and expressed via Linear Matrix Inequalities (LMI) and yields less conservative results at the expense of higher computational cost. Regarding the synthesis of Robust controllers, the following four methodologies were developed: 1. Synthesis of Robust Static State feedback 2. Synthesis of Robust Static State feedback via the “Guaranteed Cost Formulation” which combines stability and performance design objectives 3. Synthesis of Constrained Robust feedback controller (with a Piecewise Affine Structure) which respects the constraints on the control effort and the state (or output). 4. The previous result (Constrained Robust feedback controller) is then generalized for set-point tracking and for various types of network-induced delays (small, large and switching delays).

Το ερευνητικό αντικείμενο της Διατριβής είναι τα θέματα σθεναρότητας του προκύπτουν στα Δικτυωμένα Συστήματα Ελέγχου (Νetworked Cοntrοlled Systems - εφεξής "ΝCS"), όπου η βασική πηγή αβεβαιότητας είναι οι καθυστερήσεις λόγω δικτύου. Στο πλαίσιο αυτό παρουσιάζονται αποτελέσματα του αφορούν στην ανάλυση σθεναρής ευστάθειας και στην σύνθεση σθεναρών ελεγκτών. Να επισημανθεί ότι στην Διατριβή, ο προσδιορισμός "σθεναρός" αφορά αποκλειστικά σθεναρότητα (ευστάθειας και επιδόσεων) ως προς τις αβέβαιες, χρονικά μεταβαλλόμενες, φραγμένες καθυστερήσεις. Τα μελετώμενα ΝCS απαρτίζονται από την διασύνδεση γραμμικών χρονικά αμετάβλητων συστημάτων συνεχούς χρόνου με ελεγκτές διακριτού χρόνου. Η βασική διάρθρωση των συστημάτων αυτών απαρτίζεται από έναν "οδηγούμενο από χρόνο" (time driven)…