Iterative Learning Control For Uncertain Nonlinear Systems

Iterative learning control is an important part of intelligent control,which has a good tracking performance for systems with repetitive motion characteristics.It can make full use of the before control information of the system,and update the control input with the tracking error between the actual output trajectory and the expected output trajectory.After several iterations,it can track the desired trajectory completely in a given limited time interval,that is,zero error tracking.There are a lot of uncertainties in the actual system.If the uncertainties are not dealt with,the tracking performance of the system will be affected.Generally,uncertainty can be divided into two kinds:parameter uncertainty and nonparametric uncertainty.So this paper mainly studies the nonlinear systems with parametric uncertainty and nonparametric uncertainty respectively.In the analysis of nonlinear systems with parameter uncertainties,we first design an adaptive iterative learning strategy and a parameter updating rule for a class of nonlinear systems with unknown delay and unknown time-varying input gain.Then,the input saturation problem is introduced according to the saturation phenomena that may occur in the actual system.At the same time,in order to track the desired trajectory more accurately,in the presence of delay state,the current state of the system is added to make the system more available information.In this case,another adaptive iterative learning control strategy and parameter updating rule are proposed,the control strategy can deal well with the nonlinear systems with input saturation,unknown time-varying input gain,unknown time-varying delay and parameter uncertainties.By constructing Lyapunov-Krasovski composite energy function and combining with the designed adaptive iterative learning control strategy,the effectiveness of the algorithm is demonstrated by theoretical derivation and simulation.In the analysis of nonlinear systems with nonparametric uncertainties.For a class of nonlinear systems with unknown time-varying input gain and input saturation,two ideas are used to solve the nonparametric uncertainties satisfying the Lipschitz condition.The first one refers to the idea of robust control,and designs an iterative learning control strategy which is divided in two parts,the semi-saturated structure of the iterative learning part is mainly used to deal with the saturated part and the robust part is used to deal with the non-parametric uncertain part.The second one uses the properties of Lipschitz condition,adaptive iterative learning strategy and parameter updating rule to solve nonparametric uncertainties.The Lyapunov composite energy function is constructed and combined with the designed control law,the effectiveness of the algorithm is verified by theoretical analysis and simulation,and the two algorithms are compared briefly.It is impossible to have the same initial alignment in the actual system.Therefore,for a class of high-order nonlinear parameter uncertain systems,when the initial values are inconsistent,a new expected trajectory is constructed based on the initial values and the original desired trajectory,and a curve construction method is given.For high-order nonlinear systems,the tracking error convergence is controlled by constructing a sliding mode surface.Finally,the zero error tracking of the original desired trajectory is realized in a part time interval.Finally,the constructed curve and the adaptive iteration learning control algorithm are illustrated by theoretical derivation and simulation.