Switching between stabilizing controllers

Abstract

This paper deals with the problem of switching between several linear time-invariant (LTI) controllers-all of them capable of stabilizing a specific LTI process-in such a way that the stability of the closed-loop system is guaranteed for any switching sequence. We show that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system remains stable, no matter how we switch among the controller. The motivation for this problem is the control of complex systems where conflicting requirements make a single LTI controller unsuitable.

Performance optimization of piecewise affine variable-gain controllers for linear motion systems

“…To balance this trade-off in a more desirable manner, it has been shown that variable-gain control (also called N-PID control) can be effective [6][7][8][9][10][11][12]. In these references, it has been shown that the variable-gain controllers have the capability of outperforming linear controllers.…”

On controller initialization in multivariable switching systems

“…Turner & Walker (2000) assumed that both on-and off-line controllers are stabilizing for the plant in question however nothing can be concluded about stability of the overall system under arbitrary switching, Liberzon (2003). Hespanha & Morse (2002) considered the problem of selecting controller realizations and choosing initial conditions to stabilize a switched system, but no improvement in the transient response of the switching controller was considered. The optimal control problem for switched systems was considered in Xu & Antsaklis (2004) where they assume that a prespecified sequence of active subsystems is given and optimal switching times are driven.…”

“…Also Efimov et al (2010b) derive a switching law to improve the performance under stabilizing controller. Moreover, Stewart & Dumont (2006) presents a technique to improve the performance of each subcontroller in discrete time systems which is further pursued in Hespanha et al (2007) for controller initialization.…”

Controle de sistemas lineares com comutação

“…Neste caso, as condições de estabilidade devem garantir a robustez para qualquer σ(·) ∈ {1, 2, · · · , N }, sendo N a quantidade de subsistemas. Veja (Hespanha e Morse, 2002) para a síntese de controladores que estabilizam sistemas com comutação em um contexto bastante geral. O segundo grupo é caracterizado pelo fato de σ(·) ser uma variável de controle que pode, inclusive, depender do estado do sistema em estudo.…”