Optimal control of switching time in discrete-time switched autonomous system with different costs

This paper considers the optimal switching time control problem for discrete-time switched autonomous systems. The controlled parameter consists of the switching times, and the cost functional is defined on the state and performance cost functions are different in different time-intervals. Based on calculus of variations, an approach to finding the optimal switching times is proposed. Firstly, we derive the difference of the cost with respect to the switching time for one switching time case. Then, we propose an approach to deal with the problem with multi-switching times case. The obtained difference formulas have an especially simple form and can be directly used to locate the optimal switching instants. Finally, the validity of the proposed method is demonstrated by a numerical example.