Adaptive Repetitive Learning Control for a Class of Nonlinear Time-varying Systems

A novel adaptive repetitive learning control for high-order nonlinear systems with Unknown time-varying control direction and mixed parameters is proposed by combining the feedback linearization approach, It can be applied to the time-varying parametric uncertainty systems with unknown compact set, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A discrete-type adaptive law and an adaptive repetitive learning control law are constructed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm. And also, a sufficient condition of the convergence of the method is given. A simulation example illustrates the the feasibility and effectiveness of the proposed method.