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Stochastic linear quadratic regulation for discrete-time linear systems with input delay. (English) Zbl 1175.93246
Summary: This paper considers the stochastic linear Quadratic Regulation (LQR) problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels. The key to our approach is to convert the LQR control problem into an optimization one in a Hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic LQR problem by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations of the same dimension as that of the plant.
MSC:
93E20Optimal stochastic control (systems)
49N10Linear-quadratic optimal control problems
93C55Discrete-time control systems
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References:
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