Iterative Learning Control For Continuous-time Stochastic Systems

Iterative learning control(ILC)is one of the branches of intelligent control.It can obtain good tracking performance by repeating tasks and relying less on system information.The basic idea of iterative learning control is to use the previous control experience and output error of the system to modify the control input of the system,and continuously improve the tracking accuracy of the system through iteration,so as to achieve the goal of complete tracking control.In the process of actual system operation,the system state,input and output may be disturbed by random factors,so it is of great theoretical and practical significance to consider the iterative learning control problem of stochastic system.Nowadays,the ILC of stochastic systems is mainly centered at the discrete-time systems,there are few researches on iterative learning control for continuous time stochastic systems.The iterative learning control problem for continuous time stochastic systems contains two indices: continuous time and discrete iteration number,which indicates that the problem is a hybrid system.The existing convergence analysis methods for iterative learning control can be directly applied to this kind of system,so the analysis is challenging.According to the above situation,this study discusses about ILC of the continuous time stochastic system.The main content of the paper consists of the following three aspects.(1)The single input single output continuous time linear stochastic system is studied.Using the P-type iterative learning control algorithm,it is combined with formula of stochastic differential equation and Gronwall inequality.It proves that the tracking error of this system can converge bounded along the iterative axis in the sense of mean square,and the effectiveness of the algorithm is verified by numerical simulation.(2)The ILC problem for multi-input multi-output continuous time nonlinear stochastic systems is discussed.The P-type iterative learning control algorithm is selected,and the sufficient conditions for the convergence analysis of tracking errors are given.The results of bounded convergence of the tracking error in the mean square sense of the nonlinear stochastic system are obtained by using the compression mapping principle and the properties of -norm.The effectiveness of the proposed algorithm is verified by numerical simulation.(3)The ILC problem for multi-input multi-output continuous time nonlinear stochastic systems is discussed.The P-type iterative learning control algorithm is selected,and the sufficient conditions for the convergence of the tracking error in the mean square sense are given.The results of bounded convergence of the tracking error in the mean square sense of the nonlinear stochastic system are obtained by using the compression mapping principle and the properties of ?-norm.The effectiveness of the proposed algorithm is verified by numerical simulation.