Adaptive Iterative Learning Control Of Nonlinear High Order Systems

Iterative learning control is a kind of control methodology effectively dealing with repeated tracking control problems or periodic disturbance rejection problems. The basic method of traditional ILC is to achieve control input based on the previous input and the PID-revised error of previous output. After some iteration, perfect tracking can be achieved over a fixed time interval. However, the present method has some defects, such as Lipschitz continuity of nonlinear function and the dependence of convergence analysis on actually unknown ideal input, initial values resetting, As adaptive control achieves success in nonlinear uncertain systems, when the plant has of mixed parametric(time-varying and time-invariant parameters) uncertainties, the time-varying gain coefficient of iterative leaning control or non-uniform trajectories, how to make full use of the prior information and design ILC by adaptive control, it's a new subject worthwhile to research.By introducing a parametric adaptation mechanism, the adaptive control system is able to achieve asymptotic tracking convergence in the presence of constant parametric uncertainties. However, no adaptive control algorithms developed hitherto can solve unknown parameters with arbitrarily fast and non-vanishing variations.Backstepping design of nonlinear adaptive control systems is a kind of construct technique. It is based on the concept of control Lyapunov function .This kind of method overcomes the relative degree one restriction and can be used to treat the unmatched uncertainties, Therefore, it enables rigorous'analysis of systems'convergence, however, it is difficult for application in the systems with time-varying parameters uncertainties.This paper considers the ILC from an adaptive control viewpoint. Two kinds of new algorithm are proposed for ILC of essential nonlinear systems, based on Lyapunov stability theory (CEF) and backstepping technique of nonlinear system, which avoid some drawbacks and restricted assumptions of traditional ILC, The main results are as follows. Firstly, A novel adaptive iterative learning control approach is proposed for a class of hybrid parametric nonlinear systems, by means of backstepping method. The approach consisted of a differential-deference type updating law and a learning control law, can deal with the non-uniform trajectory tracking problem,which avoids the restricted on the tracking trajectory in the traditional ILC. A sufficient condition of tracking error converging to zero in the means of mean-square on the finite interval is also given by constructing a novel composite energy function. Secondly, A novel...