Multi-Period Repetitive Control for Nonparametric Uncertain Systems

This paper addresses the period-signal tracking problem for a class of nonparametric uncertain systems with several periodic time-varying disturbances, where there is no common multiple among the period lengths of reference signal and disturbances, or the common multiple is difficult to be obtained even if it exists. A multi-period repetitive control scheme is proposed by using Lyapunov approach, with robust technique and unsaturated multi-period repetitive learning technique being integratedly used to compensate uncertainties and periodic disturbances. As the repetitive cycle increases, the system output can track its reference signal perfectly over its full period. Through rigorous analysis, we prove that the estimations themselves are bounded, which is better than the boundedness in the sense of $L_{2}$ norm obtained in many existing unsaturated learning results. In the end, an illustrative examples is provided to demonstrate the efficacy of the proposed multi-period repetitive control scheme.