Adaptive repetitive control for nonlinear systems with time-varying parameters uncertainty

A design approach to the adaptive learning controller is proposed for a class of high-order nonlinear systems with time-varying and time-invariant parameters by combining the Backstepping technique with the pointwise integral mechanism. It can be applied in the time-varying parametric uncertainty systems with unknown compact set, rapid time-varying, periodic and only the prior knowledge is the periodicity. A periodic mixed adaptive law and an adaptive control law are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. And a sufficient condition of the convergence of the method is also given. A simulation example illustrates the effectiveness of the method.