Multi-controller design under uncontrolled and controlled switching

In this paper we consider the problem of designing a multi-controller K that consists of a family of stabilizing controllers {K_m}_m=1 ⁿ, where each controller K_m belongs to a constrained set K_m. Our goal is to determine the controllers {K_m}_m=1 ⁿ (and an associated switching trajectory if switching is controllable) to optimize the closed-loop system performance. Based on a special implementation of the multi-controller, the design problem under uncontrolled switching can be transformed into a sequence of convex programs, the solutions to which provide an approximate solution to the multi-controller design problem with an arbitrary given precision; while in the case of controlled switching, a heuristic method is proposed to find a suboptimal switching signal and the corresponding multi-controller. A numerical example is presented to illustrate the efficiency of the proposed algorithms.