Iterative Learning Control with Forgetting Factor Based on Initial State Learning

In the convergence of iterative learning control with the forgetting factor, the common conclusion is that output error converges to the neighborhood of zero. For analysis and to reduce the impact of the forgetting factor on system convergence error, we propose an open-loop D-type iterative learning control algorithm that incorporates the forgetting factor and the initial learning, which consist of adjacent control vectors. We then demonstrate its convergence with operator spectrum theory. On this basis, we analyze the impact of the forgetting factor on system convergence error. The proposed algorithm can eliminate the influence and expand the value range of a system's initial control vector. Multiple system information is used to effectively overcome to some extent the influence of the forgetting factor on the convergence error. The simulation results verify the validity of the proposed algorithm.