An adaptive PID-type iterative learning controller unknown nonlinear systems

To deal with an iterative learning control problem of unknown nonlinear systems with varying initial state errors and state dependent input gain, an adaptive PID-type iterative learning controller is presented in this paper. The main design concept is motivated from a fact that a PID-type controller can be used as an approximator for an optimal controller in a compact set. The main structure of the adaptive PID-type iterative learning controller is constructed based on a time-varying boundary layer, which is designed to overcome the problem of initial state errors and further eliminate the possible undesirable chattering behavior. An error equation is then derived to represent the relation between the control input and system tracking error. Since the optimal PID gains for the best approximation is in general unavailable, the control parameters are tuned between successive iterations to ensure the stability and convergence. Compared with most of the adaptive laws in the field of adaptive iterative learning control, the proposed adaptive law can be realized without using projection or dead zone mechanism. It is shown that all the adjustable parameters and the internal signals remain bounded for all iterations, and the norm of tracking error vector at each time instant would asymptotically converge to a tunable residual set.