Iterative Learning Identification and Control of Discrete Time-varying Systems

This paper presents discrete iterative learning control for systems with time-varying parametric uncertainties. Two prototype iterative learning identification algorithms, iterative learning projection and iterative learning least squares, are presented for estimating the time-varying unknowns. The main properties of the learning algorithms are explored for establishing the stability and convergence of the control scheme. The proof is based upon the use of a key technical lemma, which extends the existing one and tailored for the purpose of analysis in the iteration domain. It is shown that the complete tracking is achieved for every instant except for the initial instant, while the input and output signals of the controlled system remain bounded. The proposed scheme in this paper is applicable to tracking iteration-varying trajectories without any restriction on initial repositioning.