Adaptive approximate tracking and regulation of nonlinear systems

Presents a direct adaptive tracking control scheme for nonlinear systems that do not have a well defined relative degree and are not feedback linearizable. This technique uses feedback and coordinate changes to transform a nonlinear system with parameter uncertainty into an approximate input-output linearized one. This scheme is applicable to a wide class of nonlinear systems including slightly non-minimum phase nonlinear systems with unknown parameters, and does not constrain the growth of the nonlinearities. The authors prove that the presented adaptive design scheme results in an asymptotically stable closed loop system and show that the controller can achieve adaptive tracking of reasonable trajectories with bounds on the tracking error. The authors also present a state regulation scheme based on state approximate linearization. For regulation, unknown parameters are not restricted to appear linearly in the system dynamics