Multi-controller design under uncontrolled and controlled switching

  • Authors:

  • Shengxiang Jiang;João P. Hespanha

  • Affiliations:

  • Electrical and Computer Engineering, University of California at Santa Barbara;Electrical and Computer Engineering, University of California at Santa Barbara

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

In this paper we consider the problem of designing a multi-controller K that consists of a family of stabilizing controllers {Km}nm=1, where each controller Km belongs to a constrained set Km. Our goal is to determine the controllers {Km}nm=1 (and an associated switching trajectory if switching is controllable) to optimize the closed-loop system performance. Based on a special implementation of the multicontroller, 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.