Bang-bang control for uncertain random continuous-time switched systems

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.