A dynamic programming approach for optimal control of switched systems

In optimal control problems of switched systems, in general, one needs to nd both optimal continuous in-puts 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 prob-lem under some additional assumptions. In general, the two stage optimization problem is still diÆcult to solve analytically. In this paper, we develop a search algo-rithm to explore the solution of the two stage optimiza-tion problem and nd useful suboptimal solutions. This algorithm is motivated by the idea of dynamic program-ming which studies the value functions. The algorithm is used to determine suboptimal solutions for general switched linear quadratic problems.