Repetitive Learning Control for Control-Affine Systems With Time Delays

This article presents a repetitive learning control method, which deals with both parametric and nonparametric uncertainties involved in the control-affine systems with time delays. The desired control is taken as a time-varying parameter, and a learning algorithm is applied for estimation. The time-delay nonlinearity and the state-dependent input gain are handled as the nonparametric uncertainties, for which the adaptive bounding technique is adopted such that the requirement for the knowledge about the system undertaken can be reduced, and the troublesome time delays are effectively treated. The presented control method only needs the lower bound of the input gain is to be known as a priori. Furthermore, it is shown applicable to systems with multiple time delays. The fully saturated learning algorithms are utilized to solve the positive accumulation of estimates so that the possible divergence phenomenon can be avoided. The convergence of the tracking error is established, while the boundedness of the variables in the closed-loop system is assured. The numerical results are presented to verify the effectiveness of the proposed learning control method.