Repetitive learning control for a class of nonlinearly parameterized systems with disturbances

Combining the pointwise integral mechanism, the inequality approach with the parameter regrouping technique, a novel repetitive learning control for high-order nonlinearly parameterized systems with disturbances 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 coupled-type adaptive law and a repetitive learning control 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 and the feasibility of the proposed method.