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This paper presents a robust adaptive repetitive control (RARC) method for a class of periodically time-varying nonlinear systems with aperiodic uncertainties. A  σ  modification is introduced in the learning algorithm of RARC, in order to guarantee robustness of the system undertaken. The closed-loop type learning algorithm is examined and it is shown that the realisability cannot be assured when the  σ  modification is applied. To avoid the causality contradiction, an open-loop type learning algorithm with switching  σ  modification is proposed to guarantee robustness and achieve the asymptotic convergence of the tracking error, when the disturbances disappear. Extension to the RARC for robotic manipulators is given and the numerical simulation is carried out to verify the effectiveness of the learning control scheme.

Robust adaptive repetitive control for a class of nonlinear periodically time-varying systems