Adaptive Iterative Learning Control For Discrete-time Time-varying Nonlinear Systems

Nowadays nearly all the control algorithms are implemented digitally, consequentlydiscrete-time systems have been receiving ever increasing attention. However, in virtueof fundamental difference between discrete-time and continuous-time systems, many welldeveloped methods for continuous-time systems are not directly extended to discrete-timesystems. Adaptive control can effectively tackle the tracking problem for systems withconstant parameter uncertainties, but can hardly handle the situation when systems containtime-varying parameter uncertainties. Iterative learning control (ILC) can achieve perfecttracking task for systems running repeatedly in a finite time interval. However, the classiccontraction mapping-based ILC requires the system to satisfy some harsh conditions, suchas global Lipschitz and the initial value problem. Absorbing advantages of adaptive controland ILC, respectively, adaptive ILC can effectively deal with complete tracking problemof time-varying parameter systems. Hitherto, there are few results on discrete-time sys-tems. Discrete adaptive ILC is needed to be further investigated. In this thesis, a series ofnovel adaptive ILC schemes are developed for different kinds of discrete-time time-varyingnonlinear systems. The main work includes the following five aspects.1. Without using Nussbaum gain, a novel method is proposed to solve the unknowncontrol direction problem for a class of discrete-time time-varying SISO systems. By in-corporating two modifications into the control law and parameter update law, respectively,the control law is successfully avoided being divided by zero. Through rigorous analysis,the proposed adaptive ILC can achieve perfect tracking over the finite time interval, whileall the closed-loop signals remain bounded.2. A backstepping design of adaptive ILC is presented for a class of parametric-strict-feedback discrete-time time-varying systems. The noncausal problem in the discrete-timebackstepping design is solved by using the information in the preceding iterations. Without imposing any restrict growth conditions on the system nonlinearities, the proposed adaptiveILC can achieve perfect tracking over a finite time interval, and can guarantee the bound-edness of all the closed-loop signals.3. A backstepping-based output-feedback adaptive ILC scheme is presented for trajec-tory tracking of a class of parametric-output-feedback discrete-time time-varying nonlinearsystems. By employing an observer used to estimate the unknown states, a systematic de-sign procedure is proposed by employing information of the preceding iteration. With norestriction imposed on the system nonlinearities, the proposed adaptive ILC can guaranteeglobal stability and achieve perfect tracking over a finite time interval.4. A novel adaptive ILC design approach is presented to completely compensate non-parametric uncertainties for a class of discrete-time time-varying nonlinear systems. Usingthe iterative learning mechanism, a novel relative dead-zone algorithm is proposed to esti-mate the time-varying parameters along the iteration axis. It is rigorously proved that theproposed adaptive ILC can guarantee the boundedness of all the closed-loop signals andachieve almost perfect tracking.5. By using the iterative learning projection algorithm with dead-zone for trainingtime-varying weights, a time-varying neural networks(TVNNs) based indirect adaptive ILCscheme is presented for a class of uncertain discrete-time time-varying nonlinear systemswith unknown control gain sign. The control singularity is overcome through a modificationof the control gain estimation which can be bounded away from zero. Theoretical analysisproves the boundedness of all signals of the closed-loop system and convergence of thetracking error to a bounded region.It is worth mentioning that all the above five schemes allow that the system initialvalues and the references to be iteration-varying. The systems considered in this thesis rep-resent several general classes of discrete-time time-varying nonlinear systems. Numericalsimulations carried out verify effectiveness of the proposed control schemes.