An adaptive PID-type iterative learning controller for unknown nonlinear systems with initial state errors

In this paper, a new adaptive PID-type iterative learning controller (ILC) is proposed for a class of repeatable nonlinear systems with unknown nonlinearities. The initial state errors are allowed to be nonzero and varying for each iteration. The main structure of the adaptive PID-type ILC 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. Although the optimal gains of PID-type ILC for a best approximation are generally unknown, adaptive algorithms with projection mechanisms are derived between successive iterations to ensure the stability and convergence of the learning system. 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 will asymptotically converge to a tunable residual set.