Some Issues On Adaptive Iterative Learning Control Approaches Of Discrete-time Systems

In recent years, the scholars, in the field of automated control, have been stronglyinterested in nonlinear control theory. With the continuously enriched results ofnonlinear continuous-time systems, the study of the nonlinear discrete-time systems isfocused by the scholars. Adaptive discrete-time ILC with iteration-difference estimatorhas been presented for a class of nonlinear discrete-time systems. This methodconsiders the uncertain initial value of the system and the iteration-changed targettrajectory. This discrete adaptive ILC algorithm can solve problems of thecontinuous-time systems. However, when the plant has mixed parametricuncertainties． Using the simple discrete adaptive ILC methods only based oniteration-difference estimator in the course of each operation, the unknown parametersof the system has no update along the time axis, which will reduce the speed ofconvergence of the tracking error. In addition, all the overhead of the discrete adaptiveILC methods must meet the requirements of the linear hypothesis, in order to designdiscrete adaptive ILC. Well then, how to achieve general nonlinear systems model-freeadaptive ILC is a great research significance subject, and accord the need of practicalcontrol problems. Focusing on those problems, a new discrete adaptive ILC method isdesigned in this paper, and the research includes:Firstly, an adaptive ILC approached with a time-difference estimator is presentedfor discrete-time constant parametric uncertain systems. In the case of theiteration-varying initial value and reference trajectory, the proposed method can stillachieve full convergence of tracking error. This method is compared with the adaptivediscrete-time ILC with iteration-difference estimator. The results of the comparisonpointed out the advantages and disadvantages of the two methods and the scope oftheir applications. Let us understand the basic idea of discrete-time adaptive ILC method.Secondly, a hybrid adaptive ILC approach by introducing a hybrid adaptive ILCscheme is proposed including a time-difference estimator and an iteration-differenceestimator together for discrete-time systems in the presence of time-varying andconstant uncertain parameters. By constructing Lyapunov function to prove theconvergence of the tracking error. Simulation results show the feasibility andeffectiveness of this method.Lastly, a discrete-time adaptive ILC approach is presented for a class of generalMIMO nonlinear systems without any assumption of linearly parameterization on thenonlinearities. The uncertainty of model is inhibited, and the convergence analysis isgiven, and the feasibility of the program is proved theoretically. Simulation resultsshow that the control performance of the system can be effectively improved andenhanced by this method.