Repetitive learning control for a class of nonlinearly parameterized uncertain systems

Combining the pointwise integral mechanism with the feedback linearization approach, a novel adaptive repetitive learning control for high-order nonlinearly parameterized uncertain 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, rapid time-varying periodic and where the prior knowledge is the periodicity only, A differential-difference mixed-type adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the extended 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 and the feasibility of the proposed method.