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Adaptive Backstepping Learning Control for a Class of Nonlinear Time-Varying Systems

Combining the backstepping approach with the pointwise integral mechanism, a novel adaptive repetitive learning control for high-order nonlinear systems with time-varying and time-invariant parameters is proposed. It can be applied to the time-varying parametric uncertainty systems with unknown compact set, non-vanishing, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference 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.