Study On Rhc For Stochastic Systems With Time-Delay

This thesis is concerned with receding horizon control(RHC)problem for sever-al types of stochastic systems with input delay.An in-depth study has been made for the RHC of discrete linear time-invariant stochastic systems with single input delay,multiple input delay,linear time-varying stochastic systems with single input delay and continuous linear time-invariant stochastic systems with single input delay.Main academic contributions and innovations:Firstly,the RHC stabilization problem of linear time-invariant stochastic systems(discrete-time systems,continuous-time systems)with single input delay is resolved for the first time.A.cost function with two terminal weighting matrices is specially designed and a set of coupled Lyapunov equations are constructed.Necessary and sufficient RHC stabilization condition is given for linear time-invariant stochastic systems(discrete-time system-s,continuous-time systems)with single input delay for the first time.Under this condition,the explicit stabilizing controller is derived with the form of conditional expectation.Secondly,in order to resolve the RHC stabilization problem of discrete linear time-invariant stochastic systems with multiple input delay,a cost function with special time-varying control weighting matrices is designed.Then,the RHC stabilization condition with the form of linear matrix inequality(LMI)is obtained.In addition,the technique to construct the cost function is helpful to the study of other receding horizon stabilization problem.Thirdly,the mean square exponential stabi-lization problem of discrete linear time-varying stochastic systems with single input delay is resolved for the first time.Necessary and sufficient RHC exponential sta-bilization condition in the mean-square sense is given and the explicit stabilization controller is derived.The main contents are listed as follows in the order of chapters:1.The RHC stabilization problem for discrete linear time-invariant stochastic systems with single input delay is considered and the solving of the coupled Lya-punov inequalities is studied.For the discrete linear time-invariant stochastic sys-tems with single input delay,by designing a cost function with two terminal weight-ing matrices and analyzing the Riccati-ZXL equation,the necessary and sufficient RHC stabilization condition is obtained for the first time based on stochastic con-trol theory.It is shown that the system can be stabilized by RHC if and only if the coupled Lyapunov inequalities have solutions.In addition,two kinds of algorithm is proposed for the solving of the coupled Lyapunov inequality.One is the itera-tive algorithm which is designed by introducing a slack variable.The other is the cone complementarity linearization algorithm(CCL).The explicit RHC stabilizing controller is derived by using the maximum principle under the stabilization condi-tion.The controller is presented with the form of conditional expectation and can be obtained by solving a set of coupled Riccati difference equations.2.The RHC stabilization problem for discrete linear time-invariant stochas-tic systems with multiple input delay is investigated.By designing a cost function whose control weighting matrix is time-varying,the sufficient stabilization condition is proposed.It is shown that the system can be stabilized if the two weighting matri-ces satisfy a matrix inequality which can be transformed to an LMI.In addition,the explicit stabilizing controller is obtained.By selecting a proper horizon length,the control gain can be obtained by solving a set of simplified coupled Riccati difference equations.3.Firstly,the RHC stabilization problem for discrete linear time-varying s-tochastic systems is studied and the necessary and sufficient stabilization condition is obtained.Then,the mean square exponential stabilization problem of discrete linear time-varying stochastic systems with single input delay is investigated.By combining the advantage of receding horizon optimization and the property of cou-pled Riccati difference equation,the necessary and sufficient mean square exponen-tial stabilization condition is obtained.By analyzing the property of optimal cost function,the sufficiency is proved according to stochastic Lyapunov stability the-orem.The necessity is proved based on the coupled Lyapunov equation which is derived from analyzing the limitation of the coupled Riccati equation.The explicit stabilizing controller is derived under the stabilization condition.4.Firstly,the RHC stabilization problem for continuous linear time-varying stochastic systems is studied.Then,we studied the RHC stabilization problem of continuous linear time-invariant stochastic systems with single input delay.Com-pared with the discrete-time case,the RHC stabilization problem is more compli-cated for the continuous-time systems.By designing a new cost function,the RHC stabilization problem for continuous-time stochastic systems with single input delay is resolved for the first time.It is shown that the system can be stabilized by RHC if and only if the coupled Lyapunov inequality has solutions.The explicit stabilizing controller can be derived by solving a set of coupled Riccati differential equation under this condition.