Control of the chaotic Duffing equation with uncertainty in all parameters

In this work, we deal with the open problem of controlling the periodically forced Duffing equation with uncertainty in all parameters. To date, several control schemes have been proposed to adapt for the linearly appearing unknown parameters but no solution exists for the case when the frequency of the periodic forcing is also unknown. We prove for the state feedback control case, global, asymptotic convergence for constant and time-varying references. We extend these results to the position feedback case and prove global ultimate boundednes

Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA

A new characterisation of exponential stability

International audienceWe present a new characterization of exponential stability for nonlinear systems in the form of Lyapunov functions which may be upper and lower bounded by monotonic functions satisfying a growth order relationship rather than being polynomials of the state's norm. In particular, one may allow for Lyapunov functions with arbitrary weakly homogeneous bounds

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Speed-gradient adaptive high-gain observers for synchronization of chaotic systems

"We address the problem of output feedback synchronization of certain chaotic systems, under parameter uncertainty. That is, given a master system, the objective is to design a slave system that copies the dynamics of the master and reconstructs both the state and the values of the constant parameters of the master system. Hence, the synchronization problem that we address enters in the framework of Pecora and Carroll and relies on adaptive observer theory. In particular, the conditions that we impose take the form of persistency of excitation.

Robustness of ISS systems to inputs with limited moving average, with application to spacecraft formations

Awarded with the Best Student Paper Award in the area of Signal Processing, Systems Modeling and Control.We provide a theoretical framework that fits realistic challenges related to spacecraft formation with disturbances. We show that the input-to-state stability of such systems guarantees some robustness with respect to a class of signals with bounded average-energy, which encompasses the typical disturbances acting on spacecraft formations. Solutions are shown to converge to the desired formation, up to an offset which is somewhat proportional to the considered moving average of disturbances. The approach provides a tighter evaluation of the disturbances' influence, which allows for the use of more parsimonious control gains

Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs

We analyse the solutions of networked heterogeneous nonlinear systems. We assume that the closed-loop interconnected systems form a network with an underlying connected directed graph that contains a directed spanning tree. For these systems, we establish global uniform ultimate boundedness of the solutions, under the assumption that each agent's dynamics defines a semi-passive. As a corollary, we also establish global uniform global boundedness of the solutions

Desynchronization of coupled phase oscillators, with application to the Kuramoto system under mean-field feedback

International audienceThis note introduces two notions of desynchronization for interconnected phase oscillators by requiring that phases drift away from one another either at all times or in average. It provides a characterization of each of these two notions based on the grounded variable associated to the system, and relates them to a classical notion of instability valid in Euclidean spaces. An illustration is provided through the Kuramoto system, which is shown to be desynchronizable by proportional mean-field feedback