Adaptive iterative learning control for SISO discrete time-varying systems

An adaptive iterative learning control method is presented in this paper, for SISO time-varying discrete-time systems. In order to estimate the time-varying unknowns, two iterative learning algorithms, fully-saturated iterative learning projection algorithm and fully-saturated iterative learning least square algorithm, are given, respectively. A one-step ahead controller is developed on the basis of the certainty equivalence principle. The stability and convergence of the closed-loop system are established with the aid of the iteration-domain key technical lemma, which is a variant of the existing one, tailored for the analysis purpose in the iterative domain. The complete tracking is achieved over the pre-specified time interval excluding initial instants, as iteration goes to infinity, while all the signals in the closed-loop remain bounded.