Adaptive robust repetitive control for a class of nonlinear systems with input deadzone

In this paper, an adaptive robust repetitive controller is presented for a class of nonlinear systems with input deadzone under the condition that system nonlinear uncertainties can not be parameterized. With the assumption that the desired trajectory is periodic, the non-parametric uncertainties are written as polynomials which contain periodic time-varying parameters that are estimated by periodic learning algorithms. The unknown parameters of the deadzone are estimated by using differential adaptive algorithms, and the remained bounded error item is treated by a robust approach. To be different from the existed repetitive control, a new variable - periodic number is introduced into the robust part of the controller such that the tracking error decreases with increasing of the periodic number by the utilization of the characteristic of repetitiveness. The theoretical analysis shows that the system output is ultimately convergence to the desired periodic trajectory and all signals in the closed-loop systems are bounded.