With the advent of the modern technological age, a plethora of electronic tools and devices are available in numbers as never before. While beneficial and ex-ceedingly useful, these electronic devices require users to operate them. When designing systems capable of observing and acting upon an environment, the number of devices can become unmanageable. Previously, middleware sys-tems were designed for large-scale computational systems. However, by apply-ing similar concepts and distributing logic to autonomous agents residing on the devices, a new paradigm in distributed systems research on lightweight de-vices is conceivable. Therefore, this research focuses upon the development of a lightweight middleware that can reside on small devices enabling the capabil-ity for these devices to act autonomously. In this research, analyses determined the most advantageous methods for solving this problem. Defining a set of requirements for the necessary middle-ware as well as assumptions for the environment and system in which it would operate achieved a proper research focus. By utilizing concepts already in ex-istence such as peer-to-peer networking and distributed hash tables, devices in this system could communicate effectively and efficiently. Furthermore, creat-ing custom algorithms for communicating with other devices, and collaborating on task assignments achieved an approach to solving the consensus problem in real time. The resulting middleware solution allowed a demonstration to prove the effi-cacy. Using three devices capable of observing the environment and acting up-on it, two tests highlighted the capabilities of the consensus-finding mechanism as well as the ability of the devices to respond to changes in the environment autonomously.

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance. The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems. Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior. Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems. Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay. Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions. Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results.

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance. The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems. Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior. Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems. Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay. Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions. Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results.

Cette thèse présente une contribution sur les problèmes de contrôle de réseaux d'irrigations en tenant compte des contraintes de communication grâce à une approche multicouches d’intelligence distribuée. Les analyses détaillées de chaque couche avec les résultats analytiques et les simulations seront décrites dans les différents chapitres. Ils mettent l'accent sur l'intérêt de l'approche multicouches, plus précisément sur son efficacité et sa fiabilité pour la supervision, l'optimisation multi-objectifs et le contrôle coopératif distribué sur des systèmes complexes de transport d'eau.La première couche analysé est le réseau hydraulique composé de canaux d’écoulements à surface libre, de sous-réseaux maillés de tuyaux sous pression et des structures hydrauliques (pompes vannes, ..). En intégrant les équations de Saint-Venant pour décrire l’écoulement physique des fluides en surface libre et la méthode Lattice Boltzmann pour la simulation du fluide, nous obtenons un modèle non linéaire discret pour les canaux à surface libre. Les structures hydrauliques sont généralement traitées comme des limites internes des biefs (tronçons) et modélisées par des relations entre les variables de flux et de pression.Permettant l'échange d'informations entre les éléments du système de contrôle, le réseau de communication sera considéré comme la deuxième couche. La résolution des problèmes d’hétérogénéités des systèmes et des communications (par exemple les retards de diffusion dans le réseau, la perte de paquets, la consommation d'énergie) sera étudié en introduisant une architecture de réseau hybride avec un routage dynamique basé sur les exigences de Qualité de Service (QoS) des applications de contrôle. Pour le routage dynamique dans le réseau, une composition pondérée de certaines métriques standards est proposée afin que le protocole de routage utilisant cette métrique composite converge sans boucle avec une « route » optimum. Grâce à différents scénarios de simulation, plusieurs critères de performance du réseau ont été évalués. La comparaison des résultats de simulation permet de valider l'intérêt de cette approche de composition pour le routage dynamique.Une troisième couche propose un système de contrôle réactif optimal développé pour la régulation du réseau d'irrigation dans un modèle étendue à grande échelle : Distributed Cooperative Model Predictive Control (DCMPC). Cette partie aborde la mise en œuvre de différentes stratégies de contrôle (centralisées, décentralisées et distribuées) et intègre la communication coopérative entre les contrôleurs MPC locaux afin d’améliorer les performances global es du système. La gestion de la divergence dans l'échange d'informations entre les contrôleurs est considérée comme un problème de consensus et résolue en utilisant un protocole de consensus asynchrone. Cette approche du contrôle distribué basée sur le paradigme des systèmes multi-agents, fournit une solution garantissant que tous les contrôleurs aient une vue cohérente de certaines valeurs des données nécessaires pour le calcul de décision. Un cas d’application sur un canal d'irrigation est étudié dans les simulations. La comparaison des résultats de simulations valide les avantages de l'approche du contrôle distribué coopératif par rapport aux autres stratégies de contrôle. / This thesis presents control problems of irrigation network with communication constraints and a multi-layer approach to solve these problems in a distributed manner. Detailed discussions of each layer with analytical and simulation results are described throughout several chapters. They emphasize the potential interest of the multi-layer approach, more precisely its efficiency and reliability for supervision, multi-objective optimization and distributed cooperative control of complex water transport systems. Conventionally, the first layer to be considered is the hydraulic network composed of free-surface channels, hydraulic structures and mesh subnetwork of pressurized pipes. By coupling the Saint-Venant equations for describing the physics of free-surface fluid and the Lattice Boltzmann method for the fluid simulation, a discrete-time nonlinear model is obtained for channel reaches. The hydraulic structures are usually treated as internal boundaries of reaches and modeled by algebraic relationships between the flow and pressure variables. To enable the exchange of information among the control system’s components, a communication network is considered in the second layer. Solving challenging problems of heterogeneous devices and communication issues (e.g., network delay, packet loss, energy consumption) is investigated in this thesis by introducing a hybrid network architecture and a dynamic routing design based on Quality of Service (QoS) requirements of control applications. For network routing, a weighted composition of some standard metrics is proposed so that the routing protocol using the composite metric achieves convergence, loop-freeness and path-optimality properties. Through extensive simulation scenarios, different network performance criteria are evaluated. The comparison of simulation results can validate the interest of this composition approach for dynamic routing. Finally, the third layer introduces an optimal reactive control system developed for the regulatory control of large-scale irrigation network under a Distributed Cooperative Model Predictive Control (DCMPC) framework. This part discusses the implementation of different control strategies (e.g., centralized, decentralized, and distributed strategies) and how the cooperative communication among local MPC controllers can be included to improve the performance of the overall system. Managing divergent (or outdated) information exchange among controllers is considered in this thesis as a consensus problem and solved by an asynchronous consensus protocol. This approach based on the multi-agent system paradigm to distributed control requires each controller to agree with its neighbors on some data values needed during action computation. For simulations, a particular benchmark of an irrigation channel is considered. The comparison of simulation results validate the benefits of the distributed cooperative control approach over other control strategies.

Les sujets discutés dans cette thèses’inscrivent dans le cadre général des systèmesinterconnectés. Nous abordons les réseauxmulti-agent qui ont des tâches coopératives etnous proposons un nouveau protocole deconsensus qui comporte des retards et desagents anticipatifs. Nous étudions lesconditions pour lesquelles un réseau organiséconformément au protocole proposé atteint leconsensus. Nous dérivons également desrésultats théoriques valables pour une classeplus générale de systèmes. Ces résultatsconcernent le cas des racines multiples surl’axe des imaginaires, situation qui peutcorrespondre aux réseaux avec une topologiechangeante.Dans notre approche, nous discutonsséparément le cas des racines multiples àl’origine et racines multiples sur l’axe desimaginaires sauf l’origine. Un autre résultatimportant comporte un nouveau modèle pourun réseau génétique qui fonctionne comme unmultiplexeur. Ce circuit innovant utilise troisentrées pour commander deux signaux desortie. Nous effectuons une analyse destabilité pour le modèle proposé et nousdémontrons que son point d’équilibre estunique et stable. Pour valider ce réseaugénétique, nous étudions également le modèlestochastique dérivé du modèle déterministe. / This thesis discusses diverse types ofinterconnected systems through networks. Weaddress networks of agents with cooperativetasks and propose a new consensus protocolwith delays and anticipatory agents. We studythe consensus reaching conditions for networksorganized under the proposed model.Moreover, we derive some theoretical results,which can apply to a more general class ofsystems, concerning stability issues when theconsidered system has multiple imaginaryroots. In terms of networks, this situation cancorrespond to the case of switching topologynetworks, when the network can even bedisconnected at some point.We separately discuss the case of zerocharacteristic roots, and roots laying on theimaginary axis, except the origin. Finally, wepropose a gene network model with afunctionality similar to a multiplexer circuit.Thus, we control two outputs with three inputsignals, and we carry out a stability analysis.We prove the uniqueness and the stability ofthe network steady states, and validate thecontinuous and deterministic model with astochastic model.

<p>The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.</p><p>The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.</p><p>Direct methods for trajectory optimization are traditionally based on<i> a</i> <i>priori </i>temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.</p><p>In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.</p><p>Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming <i>a</i> <i>priori </i>bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.</p>

The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively. The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example. In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors. Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20101108