P-type iterative learning control of nonlinear systems with uncertainties

This paper deals with the problem of robustness of P-type iterative learning control for uncertain nonlinear system. Besides the vector field, the control matrix and output matrix of the control system considered in this paper all have uncertainties. Iterative learning laws for initial states and for inputs are presented. A new technique has been developed to estimate the tracking errors of iterative control systems, which have an initial state error. Based on the estimation, upper bounds of the norms of the uncertainties of the control matrix and the output matrix are obtained, which guarantee that the iterative learning laws for initial states and for inputs are convergent. The results in this paper show that the P-type iterative learning control has robustness with respect to the uncertainties of the control matrix and the output matrix.