Constrained Control for Time - Delay Systems

Ecole Superieure d’Eletricité SUPELEC Systems Sciences (E3S) Automatic Control Department and Laboratory of Signals and Systems, CNRS-SUPELEC Doctor of Sciences in Physics by Warody Claudinei Lombardi The main interest of the present thesis is the constrained control of time-delay system, more specifically taking into consideration the discretization problem (due to, for example, a communication network) and the presence of constraints in the system’s trajectories and control inputs. Time-delay systems are largely used to describe some physical phenomena, where the reaction of the system with respect to exogenous signals is not instantaneous. For continuous-time systems controlled by a network (called networked control systems), the problem becomes interesting due to the network-induced delays and to the discretization problem (the delays can vary between the sampling instants). The effects of data-sampling and modeling problem are studied in detail, where an uncertainty is added into the system due to additional effect of the discretization and delay. The delay variation with respect to the sampling instants is characterized by a polytopic supra-approximation of the discretization/delay induced uncertainty. The discretized system can be expressed in terms of an augmented (or extended) state-space system. Three cases are studied, depending on the structure of the eigenvalues of the system matrices. In order to decrease the conservativeness of these basic results, some methods and algorithms are proposed in order to obtain an improved polytopic model. Some stabilizing techniques, based on Lyapunov’s theory, are then derived for the unconstrained case. In an augmented state-space case, by using simple quadratic Lyapunov candidates, a extended state-feedback gain is obtained by using LMI techniques. Lyapunov-Krasovskii candidates were also used to obtain LMI conditions for a statefeedback, in the “original” state-space of the system. For the constrained control purposes, the set invariance theory is used intensively, in order to obtain a region where the system is “well-behaviored”, despite the presence of constraints and (time-varying) delay. Due to the high complexity of the maximal delayedstate admissible set obtained in the augmented state-space approach, in the present te l-0 06 31 50 7, v er si on 2 10 J an 2 01 3