Global disturbance rejection of a class of nonlinear systems with unknown exosystems

An asymptotic rejection algorithm is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown disturbances. The disturbances are generated from an unknown exosystem, and are assumed to be sinusoidal disturbances with unknown amplitude and frequency. By using the technique of backstepping and adaptive control, a nonlinear state feedback controller is designed. Under the proposed controller, the system’s state variables asymptotically converge to zero, and the disturbances are rejected completely. The approach used is an integration of the robust stabilization technique, adaptive technique, and backstepping technique.