# American Institute of Mathematical Sciences

2009, 5(4): 737-747. doi: 10.3934/jimo.2009.5.737

## Optimal control of piecewise affine systems with piecewise affine state feedback

 1 Department of Mathematics, Chongqing Normal University, Shapingba, Chongqing, 400047, China 2 Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845 3 Department of Mathematics and Statistics, Curtin University of Technology, Perth, 6002, WA, Australia

Received  May 2008 Revised  May 2009 Published  August 2009

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.
Citation: Changzhi Wu, Kok Lay Teo, Volker Rehbock. Optimal control of piecewise affine systems with piecewise affine state feedback. Journal of Industrial & Management Optimization, 2009, 5 (4) : 737-747. doi: 10.3934/jimo.2009.5.737
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