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Linear quadratic regulation for discrete-time systems with multiplicative noise and multiple input delays. (English) Zbl 1366.93704
Summary: This paper is concerned with the optimal linear quadratic regulation problem for discrete-time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state.

MSC:
93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
93C55 Discrete-time control/observation systems
93B52 Feedback control
49K45 Optimality conditions for problems involving randomness
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