In this paper, optimal control problems concerning uncertain random continuous-time switched system were studied. First, by applying Belleman's principle of optimality and chance theory, an optimality equation was derived. It's an extension of the equation of optimality from uncertain environment to uncertain random environment. Then, the optimality equation was employed to get bang-bang control for the control problems with the linear performances. Second, a two-stage algorithm was applied to implement optimal control. A genetic algorithm and Brent algorithm were used in the second stage in order to search the optimal switching instants in the numerical example. Finally, as an application of our theoretical results, an optimal cash holding problem was discussed and a corresponding optimal cash holding level was provided.

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.