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Singular linear quadratic optimal control for singular stochastic discrete-time systems. (English) Zbl 1302.93239

Summary: The finite time horizon singular linear quadratic (LQ) optimal control problem is investigated for singular stochastic discrete-time systems. The problem is transformed into positive LQ one for standard stochastic systems via two equivalent transformations. It is proved that the singular LQ optimal control problem is solvable under two reasonable rank conditions. Via dynamic programming principle, the desired optimal controller is presented in terms of matrix iterative form. One simulation is provided to show the effectiveness of the proposed approaches.

MSC:

93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
49N10 Linear-quadratic optimal control problems
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