Repetitive learning finite-time control

This paper presents a method of the repetitive learning finite-time controller design, with the use of adaptive robust control technique. Through Lyapunov synthesis, the learning controller is designed, and the finite-time convergence performance is realized by applying the terminal attracting technique, which, in comparison, improves the tracking performance by applying the asymptotic tracking method. The full saturation is introduced in the learning algorithm for estimating the time-varying parametric uncertainties, and boundedness of the estimates is obtained. It is shown that as time increases the tracking error will be remained within a pre-specified region, by which the transient performance can be guaranteed, and converge to a neighborhood of origin, with the radius given in advance. The numerical results are presented to demonstrate effectiveness of the proposed learning control scheme.