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Receding Horizon Control-Based Stabilization of Discrete-Time Stochastic Systems With State Delay

The stabilization of receding horizon control (RHC) for a class of discrete-time stochastic systems with multiple state delay is concerned. Firstly, a cost function with the type of conditional expectation is designed. Secondly, the sufficient RHC stabilization condition has been obtained in terms of a linear matrix inequalities (LMI). And under some appropriate assumptions, it is shown that the stochastic system with state delay can be stabilized in the mean square sense if the terminal weighting matrices satisfy the given inequalities. Lastly, the explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Numerical examples show that the proposed RHC can effectively stabilize stochastic systems with state delay.