Optimal piecewise state feedback control for impulsive switched systems

Authors:
R. Li;Z. G. Feng;K. L. Teo;G. R. Duan
Affiliations:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, PR China;College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, PR China;Department of Mathematics & Statistics, Curtin University of Technology, Perth, WA 6845, Australia;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

In this paper, we consider a class of the optimal state feedback control problems involving switched systems with state jumps. The planning time horizon is subdivided into N subintervals, where the breakpoints are called the re-setting times. One system is used during each subinterval with a piecewise state feedback control form. The re-setting time, the feedback gain matrices and the heights of the state jumps at the re-setting times are considered as decision variables. It is shown, through a time scaling transform, that this class of optimal control problems is equivalent to an optimal parameter selection problem, where the varying re-setting time points are mapped into fixed time points. The gradient formula of the transformed cost function is derived. With this gradient formula, the optimal parameter selection problem can be solved as a nonlinear optimization problem, and the optimal control software MISER 3.3 can be used. Two illustrative examples are solved using the proposed method.