Feedback-Aided PID-type Iterative Learning Control against Initial State Error

This paper presents a PID-type ILC (iterative learning control) algorithms for system which undertaken performance tasks repetitively over a pre-specified finite-time interval in the presence of initial state error, and the convergence analysis shows that the tracking error converges to zero asymptotically as time goes to infinity. Furthermore, a kind of initial rectifying strategy is addressed to eliminate the effect of the fixed initial state error, and the limit trajectory is stated. At last, numerical results are addressed to demonstrate the validity of the proposed learning control algorithms.