Initial condition issues on iterative learning control for non-linear systems with time delay

Most of the available results on iterative learning control address traject ory tracking problem for systems without time delay. The role of the initia l function in tracking performance of iterative learning control for system s with time delay is not yet fully understood. In this paper, asymptotic pr operties of a conventional learning algorithm are examined for a class of n on-linear systems with time delay in the presence of initial function error s. It is shown that a non-zero initial function deviation can cause a lasti ng tracking error on the entire operation. Impulsive action is one method t o eliminate such lasting tracking error but it is not a practical approach. As an alternative, an initial rectifying action is introduced in the learn ing algorithm. The initial rectifying action is finite and used over a spec ified interval. It is shown to be effective in the improvement of tracking performance, in particular robustness and uniform convergence. The results are further extended to systems with multiple time delays. An example is gi ven and computer simulations are presented to demonstrate the performance o f the proposed approach.