Abstract
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.
Highlights
With the rapid development of science and technology, more and more complex systems appear, such as communication systems, power systems, multi-agent systems and so on [1]
RHC was developed to stochastic linear systems with both input and state multiplicative noise in [21], as well as a result characterizing stochastic stability for the receding horizon controlled system under a specific choice of terminal weight and terminal constraint was provided
The main contributions of this paper are summarized as follows: (1) motivated by [23], [24], a conditional expectation type cost function is constructed in order to obtain the stabilizing conditions; (2) the explicit RHC controller for system stabilization is proposed by solving the finite horizon optimal control problem; and (3) by means of linear matrix inequality (LMI), sufficient condition for stabilization of stochastic systems with state delay is obtained for the first time by making the optimal performance index decrease monotonically
Summary
With the rapid development of science and technology, more and more complex systems appear, such as communication systems, power systems, multi-agent systems and so on [1]. RHC was developed to stochastic linear systems with both input and state multiplicative noise in [21], as well as a result characterizing stochastic stability for the receding horizon controlled system under a specific choice of terminal weight and terminal constraint was provided. The main contributions of this paper are summarized as follows: (1) motivated by [23], [24], a conditional expectation type cost function is constructed in order to obtain the stabilizing conditions; (2) the explicit RHC controller for system stabilization is proposed by solving the finite horizon optimal control problem; and (3) by means of linear matrix inequality (LMI), sufficient condition for stabilization of stochastic systems with state delay is obtained for the first time by making the optimal performance index decrease monotonically.
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