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Optimal Timing Control of Discrete-Time Linear Switched Stochastic Systems

Xiaomei Liu*, Kanjian Zhang, Shengtao Li, Shumin Fei, and Haikun Wei
International Journal of Control, Automation, and Systems, vol. 12, no. 4, pp.769-776, 2014

Abstract : Optimal switch-time control is the study that investigates how best to switch between different modes. In this paper, we investigate the optimal switch-time control problem for discrete-time linear switched stochastic systems. In particular, under the assumption that the sequence of active subsystems is pre-specified, we focus on the problem where the objective is to minimize a cost functional defined on the states and the switching times are the only control variables. For systems with one switching time, using calculus of variations, we firstly derive the difference formulae of the cost functional with respect to the switching time, which can be directly used to find the optimal switching instant. Then, a method is presented to deal with the problem with multiple switching times case. Finally, the viability of the proposed method is illustrated through two numerical examples.

Keyword : Calculus of variation, discrete time, optimal control, switched stochastic systems.

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