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Almost sure tracking for linear discrete-time periodic systems with independent random perturbations. (English) Zbl 1152.93482

Summary: In this paper we solve the tracking problem for linear discrete-time periodic systems with independent random perturbations in Hilbert spaces. Under stabilizability and either uniform observability or detectability conditions we find the optimal control which minimizes the cost function associated to this problem. We extend the results from A. Halanay, T. Morozan and C. Tudor [Int. J. Control 47, No. 1, 381–392 (1988; Zbl 0642.93068)] to the general case where the stochastic perturbations act both on the state and control variables. We also establish the connection between the uniform observability and the tracking problem.

MSC:

93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
93E20 Optimal stochastic control
93C05 Linear systems in control theory

Citations:

Zbl 0642.93068
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