Robust adaptive repetitive control for periodically time-varying systems

In this paper, a robust adaptive repetitive control algorithm is presented for periodically time-varying systems. The periodically time-varying parameters are estimated by periodic learning algorithms, and the non-periodic uncertainties are treated by robust adaptive approaches. Different from the existing repetitive control, a new variable periodic number is introduced to the control design. When this number increases, the convergence error will gradually decrease due to the repetition character of the periodic system, so that the global asymptotic stability is ensured. Further, this method is applied to a class of nonlinearly parameterized systems with non-parametric disturbances, and the tracking error converges asymptotically. This result is verified by a simulation of an invert pendulum model. Moreover, it is proven that the proposed design method is appropriate for the elimination of influence of approximation error of neural network. A theoretical analysis shows that the system output is convergent to the desired one and all signals in the network based robust adaptive repetitive control system are bounded. The simulation result of robotic manipulators shows a good tracking performance of the controlled system. ©, 2014, Acta Automatica Sinica. All rights reserved.