Journal of Industrial and Management Optimization (JIMO)

Optimal control of piecewise affine systems with piecewise affine state feedback

Pages: 737 - 747, Volume 5, Issue 4, November 2009      doi:10.3934/jimo.2009.5.737

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Changzhi Wu - Department of Mathematics, Chongqing Normal University, Shapingba, Chongqing, 400047, China (email)
Kok Lay Teo - Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845, Australia (email)
Volker Rehbock - Department of Mathematics and Statistics, Curtin University of Technology, Perth, 6002, WA, Australia (email)

Abstract: In this paper, we consider a class of optimal control problems involving piecewise affine (PWA) systems with piecewise affine state feedback. We first show that if the piecewise affine state feedback control is assumed to be continuous at the switching boundaries, then the number of switching amongst PWA systems is finite. On this basis, this optimal control problem is transformed into a discrete valued optimal control problem. For this discrete valued optimal control problem, we introduce the time scaling transform to convert it into an equivalent constrained optimal parameter selection problem, for which it can be solved by existing optimal control techniques for optimal parameter selection problems. A numerical example is solved so as to illustrate the proposed method.

Keywords:  Piecewise affine system; State feedback; Optimal control.
Mathematics Subject Classification:  34H05, 49M37.

Received: May 2008;      Revised: May 2009;      Available Online: August 2009.