Abstract: A novel adaptive repetitive learning control for second-order nonlinear systems with time-varying and time-invariant parameters is proposed by using the Backstepping approach. It can be applied to the time-varying parametric uncertainty systems with an unknown compact set, which are non-vanishing, rapid time-varying, and periodic and where the prior knowledge is the periodicity only. A periodic mixed adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition for the convergence of the method is given. A simulatioin example illustrates the effectiveness and the feasibility of the proposed method.

Key words: adaptive repetitive learning control, Backstepping approach, Lyapunov function, periodic parameter adaptive law, mixed parametric nonlinear system