OPTIMAL SWITCHING TIME CONTROL OF DISCRETE-TIME SWITCHED AUTONOMOUS SYSTEMS

Optimal switching time control is the study that investigates how best to switch between different modes. In this paper, we present an approach for solving the optimal switching time control problem of discrete-time switched linear systems, where the objective is to minimize a cost functional defined on the state. In particular, we assume that the sequence of active subsystems is pre-specified and the switching times are the only control variables. Firstly, using calculus of variations, for one switching time case, the difference of the cost with respect to the switching time is derived. Then, a method is provided to deal with the switched systems with multiple switching times. It is worth mentioning that the differences of the cost functional have an especially simple form and can be easily used to locate the optimal switching instants. Finally, a numerical example shows the viability of the proposed method.

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