Adaptive Repetitive Control for a Class of Nonlinearly Parametrized Systems

In this note, Lyapunov-based adaptive repetitive control is presented for a class of nonlinearly parametrized systems. Through the use of an integral Lyapunov function, the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control. Global stability of the adaptive system and asymptotic convergence of the tracking error are established, and tracking error bounds are provided to quantify the control performance. Both partially and fully saturated learning laws are analyzed in detail, and compared analytically