Uncertain random problem for multistage switched systems

Optimal control problems for switched systems how best to switch between different subsystems. In this paper, two kinds of linear quadratic optimal control problems for multistage switched systems composing of both randomness and uncertainty are studied. Chance theory brings us a useful tool to deal with this indeterminacy. Based on chance theory and Bellman's principle, the analytical expressions are derived for calculating both the optimal control input and the optimal switching control law. Optimal control is implemented by genetic algorithm instead of enumerating all the elements of a series of sets whose size grows exponentially. Finally, the results of numerical examples are provided to illustrate the effectiveness of the proposed method.