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

Most of the available results on iterative learning control address trajectory tracking problem for systems without time delay. The role of the initial function in tracking performance of iterative learning control for systems with time delay is not yet fully understood. In this paper, asymptotic properties of a conventional learning algorithm are examined for a class of non-linear systems with time delay in the presence of initial function errors. It is shown that a non-zero initial function deviation can cause a lasting tracking error on the entire operation. Impulsive action is one method to eliminate such lasting tracking error but it is not a practical approach. As an alternative, an initial rectifying action is introduced in the learning algorithm. The initial rectifying action is finite and used over a specified 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 given and computer simulations are presented to demonstrate the performance of the proposed approach.