A Unified Design Approach to Repetitive Learning Control for Systems Subject to Fractional Uncertainties

Abstract

Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.