Repetitive Learning Control for Nonlinear Systems Subject to Time Delays

This paper presents a repetitive learning control scheme for a class of nonlinear systems with time-delay nonlinearities and fractional uncertainties. The control design is conducted through the direct parametric estimation and the adaptive bounding technique. The desired control input is taken as the parametric uncertainty with regressor one, and the direct estimation is adopted. The time-delay nonlinearity with the fractional uncertainty is tackled as the nonparametric uncertainty, where the bounding function is learned in order to reduce the requirement for the knowledge about the system dynamics. The upper bound of the control input gain is the only prior information requested in this scheme. The convergence of the tracking error is obtained and the boundedness of the variables in the closed-loop system is guaranteed. The numerical simulations are carried out to illustrate the effectiveness of the proposed RLC scheme.