Receding Horizon Control For Discrete-time Stochastic Systems With Time-delay

The problem of receding horizon control(RHC)for a class of discrete-time stochastic systems with time delay is studied in this paper.RHC stabilization control for discrete-time stochastic systems with state delay,singular stochastic systems with state delay,and singular stochastic systems with input delay are studied in detail.Main contributions and innovations are as follows: Firstly,a cost function in the form of conditional expectation is constructed,and a sufficient condition for stabilization of stochastic systems with state delay is obtained by designing a weighted terminal matrix to make the cost function monotonically decreasing.Secondly,in the process of solving an optimal control problem in finite horizon,the relationship between costate and state is established by using the extremum principle and linear quadratic regulation(LQR)method.An explicit RHC stabilization controller is obtained by solving a set of coupled forward and backward stochastic difference equations with time delay.Thirdly,by solving an optimal control problem in the finite horizon,the sufficient and necessary conditions for the existence of a unique solution to the optimal control problem for singular stochastic systems with time delay are given on the premise of regularity and no pulse satisfaction.The main contents are stated as follows:1.The RHC stabilization problem for discrete-time stochastic systems with state delay is studied.A cost function in the form of conditional expectation is constructed,and a sufficient condition for stabilization is obtained that the weighted matrix in the cost function satisfies the given matrix inequality,which can be solved by transforming to linear matrix inequality.An explicit RHC stabilization controller is obtained by using the extremum principle and the LQR method.2.The RHC stabilization problem for discrete-time singular stochastic systems with state delay is studied.Compared with the previous studies,RHC stabilization control for discrete-time singular stochastic systems with state delay and multiplicative noise is more complex.Under the condition of satisfying the regularity and no pulse,establishing the relationship between the costate and state by the extremum principle,and deducing the necessary and sufficient conditions for the existence of a uniquesolution to the optimal control problem are the key and difficult points of this chapter.The RHC stabilization controller is a linear function of the current state and the historical state.3.The RHC stabilization problem for discrete-time singular stochastic systems with input delay is studied.Different from the above research,this chapter considers the input delay,the costate obtained by the extremum principle is a linear function of the current state and the historical input,so the cost function constructed is different from the previous one.The cost function not only contains a terminal weighted matrix of the state,but also a terminal weighted matrix of the historical input.The RHC stabilization controller is a linear function of current state and historical input under the conditions of regularity,no pulse and stabilization.