Leaderless synchronization of heterogeneous oscillators by adaptively learning the group model

International audienc

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Interval Observer Approach to Output Stabilization of Time-Varying Input Delay System

International audienceThe output stabilization problem for a linear system with a time-varying input delay is considered. The interval observer technique is extended to delay control systems and applied for obtaining guaranteed interval estimates of the system state. The procedure of the interval observer design, which is based on resolving of the Silvester's equation, is presented. Interval predictor method is introduced in order to design a linear stabilizing feedback. The control design procedure is based on Linear Matrix Inequalities (LMI). The theoretical results are supported by numerical simulations

Robust control strategies for unstable systems with input/output delays

Los sistemas con retardo temporal aparecen con frecuencia en el ámbito de la ingeniería, por ejemplo en transmisiones hidráulicas o mecánicas, procesos metalúrgicos o sistemas de control en red. Los retardos temporales han despertado el interés de los investigadores en el ámbito del control desde finales de los años 50. Se ha desarrollado una amplia gama de herramientas para el análisis de su estabilidad y prestaciones, especialmente durante las dos últimas décadas. Esta tesis se centra en la estabilización de sistemas afectados por retardos temporales en la actuación y/o la medida. Concretamente, las contribuciones que aquí se incluyen tienen por objetivo mejorar las prestaciones de los controladores existentes en presencia de perturbaciones. Los retardos temporales degradan, inevitablemente, el desempeño de un bucle de control. No es de extrañar que el rechazo de perturbaciones haya sido motivo de estudio desde que emergieron los primeros controladores predictivos para sistemas con retardo. Las estrategias presentadas en esta tesis se basan en la combinación de controladores predictivos y observadores de perturbaciones. Estos últimos han sido aplicados con éxito para mejorar el rechazo de perturbaciones de controladores convencionales. Sin embargo, la aplicación de esta metodología a sistemas con retardo es poco frecuente en la literatura, la cual se investiga exhaustivamente en esta tesis. Otro inconveniente de los controladores predictivos está relacionado con su implementación, que puede llevar a la inestabilidad si no se realiza cuidadosamente. Este fenómeno está relacionado con el hecho de que las leyes de control predictivas se expresan mediante una ecuación integral. En esta tesis se presenta una estructura de control alternativa que evita este problema, la cual utiliza un observador de dimensión infinita, gobernado por una ecuación en derivadas parciales de tipo hiperbólico.Time-delay systems are ubiquitous in many engineering applications, such as mechanical or fluid transmissions, metallurgical processes or networked control systems. Time-delay systems have attracted the interest of control researchers since the late 50's. A wide variety of tools for stability and performance analysis has been developed, specially over the past two decades. This thesis is focused on the problem of stabilizing systems that are affected by delays on the actuator and/or sensing paths. More specifically, the contributions herein reported aim at improving the performance of existing controllers in the presence of external disturbances. Time delays unavoidably degrade the control loop performance. Disturbance rejection has been a matter of concern since the first predictive controllers for time-delay systems emerged. The key idea of the strategies presented in this thesis is the combination of predictive controllers and disturbance observers. The latter have been successfully applied to improve the disturbance rejection capabilities of conventional controllers. However, the application of this methodology to time-delay systems is rarely found in the literature. This combination is extensively investigated in this thesis. Another handicap of predictive controllers has to do with their implementation, which can induce instability if not done carefully. This issue is related to the fact that predictive control laws take the form of integral equations. An alternative control structure that avoids this problem is also reported in this thesis, which employs an infinite-dimensional observer, governed by a hyperbolic partial differential equation.Sanz Díaz, R. (2018). Robust control strategies for unstable systems with input/output delays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/111830TESI

Output Consensus Control for Heterogeneous Multi-Agent Systems

We study distributed output feedback control of a heterogeneous multi-agent system (MAS), consisting of N different continuous-time linear dynamical systems. For achieving output consensus, a virtual reference model is assumed to generate the desired trajectory for which the MAS is required to track and synchronize. A full information (FI) protocol is assumed for consensus control. This protocol includes information exchange with the feed-forward signals. In this dissertation we study two different kinds of consensus problems. First, we study the consensus control over the topology involving time delays and prove that consensus is independent of delay lengths. Second, we study the consensus under communication constraints. In contrast to the existing work, the reference trajectory is transmitted to only one or a few agents and no local reference models are employed in the feedback controllers thereby eliminating synchronization of the local reference models. Both significantly lower the communication overhead. In addition, our study is focused on the case when the available output measurements contain only relative information from the neighboring agents and reference signal. Conditions are derived for the existence of distributed output feedback control protocols, and solutions are proposed to synthesize the stabilizing and consensus control protocol over a given connected digraph. It is shown that the H-inf loop shaping and LQG/LTR techniques from robust control can be directly applied to design the consensus output feedback control protocol. The results in this dissertation complement the existing ones, and are illustrated by a numerical example. The MAS approach developed in this dissertation is then applied to the development of autonomous aircraft traffic control system. The development of such systems have already started to replace the current clearance-based operations to trajectory based operations. Such systems will help to reduce human errors, increase efficiency, provide safe flight path, and improve the performance of the future flight

Flat systems, equivalence and trajectory generation

3rd cycleIntroduction : Control systems are ubiquitous in modern technology. The use of feedback control can be found in systems ranging from simple thermostats that regulate the temperature of a room, to digital engine controllers that govern the operation of engines in cars, ships, and planes, to flight control systems for high performance aircraft. The rapid advances in sensing, computation, and actuation technologies is continuing to drive this trend and the role of control theory in advanced (and even not so advanced) systems is increasing..

Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems

A static non-linear homogeneous feedback for a fixed-time stabilization of a linear time-invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial conditions. The constant convergence time is achieved due to a dependence of the feedback gain of the initial state of the system. The robustness of the closed-loop system with respect to measurement noises and exogenous perturbations is studied using the concept of Input-to-State Stability (ISS). Both delay-free and input delay systems are studied. Theoretical results are illustrated by numerical simulations

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control