Optimal control of discrete-time switched linear systems via continuous parameterization

The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly minimize a quadratic performance index. State-of-art methods for solving such a control problem suffer in general from a high computational requirement due to the fact that an exponential number of switching sequences must be explored. The method of this paper addresses the challenge of the switching law design by introducing auxiliary continuous input variables and then solving a non-smooth block-sparsity inducing optimization problem.Comment: 6 pages, 2 figures, 2 tables; To appear in the Proceedings of IFAC World Congress, 201

Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.Comment: 19 pages, 3 figure

Robust Stability Analysis for Uncertain Switched Discrete-Time Systems

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes