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.

本文提出了一类具有非周期性不确定性的周期性时变非线性系统的鲁棒自适应重复控制（RARC）方法。一个σ修改在RARC的学习算法介绍，为了进行系统的保障鲁棒性。对闭环型学习算法进行了检验，结果表明，当应用σ修正时，不能保证可实现性。为避免因果矛盾，一种切换σ的开环式学习算法当干扰消失时，提出修改以保证鲁棒性并实现跟踪误差的渐近收敛。给出了机器人机械手 RARC 的扩展，并进行了数值模拟以验证学习控制方案的有效性。