A Dynamic Programming Approach for Optimal Control of Switched Systems

X.Xu and P.J. Antsaklis

Proceedings of the 2000 Conference on Decision and Control
pp. 1822-1827. Sydney, Ausralia, December 12-15, 2000.

Abstract- In optimal control problems of switched systems, in general, one needs to nd both optimal continuous inputs and optimal switching sequences, since the system dynamics vary before and after every switching instant. In a previous paper, we proved that an optimal control problem can be posed as a two stage optimization problem under some additional assumptions. In general, the two stage optimization problem is still difficult to solve analytically. In this paper, we develop a search algorithm to explore the solution of the two stage optimization problem and nd useful suboptimal solutions. This algorithm is motivated by the idea of dynamic programming which studies the value functions. The algorithm is used to determine suboptimal solutions for general
switched linear quadratic problems.

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