Universal Repetitive Learning Control for Nonparametric Uncertainty and Unknown State-Dependent Control Direction Matrix

We propose a continuous universal repetitive learning control to track periodic trajectory for a class of nonlinear dynamical systems with nonparametric uncertainty and unknown state-dependent control direction matrix. The proposed controller is an integration of high-gain feedback, repetitive learning and Nussbaum gain matrix selector. The control signal is always continuous, thus it avoids the potential chattering effect caused by discontinuity. Asymptotic convergence of the tracking error is achieved by the controller, and the control performance is illustrated by simulation. Although the proposed method is derived for input-state systems, it can be readily extended to multi-input-multi-output systems under appropriate assumption.