Adaptive Learning Control for Nonlinear Systems With Parametric and Non-Parametric Uncertainties

A repetitive learning control scheme is designed for nonlinear systems with parametric and non-parametric uncertainties. It is assumed that the common periodicity of unknown time-varying parameter and reference signal are known a prior. By regrouping the system parameters, all unknown time-varying terms are combined into a periodically time-varying vector. Combining the modifying backstepping approach with the pointwise integral mechanism, a differential-difference mixed-type 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 of the convergence of the method is given. A simulation example illustrates the effectiveness of the proposed method.