Adaptive rejection of periodic & non-periodic disturbances for a class of nonlinearly parametrized systems

In this paper, Lyapunov-based adaptive control is presented for a class of nonlinearly parametrized systems in the presence of periodic disturbances. 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. Both 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 analytically.