Output Tracking for Nonlinear Systems with Uncertainities

In this paper we study the problem of output tracking for a class of single-input single-output minimum-phase nonlinear systems in the presence of uncertainities. Given a bounded desired tracking signal with bounded derivatives, a control law is designed which results in tracking of the signal by the output. In the presence of uncertainities in the model vector field, the designed control law is modified so that the effect of uncertainities on the tracking error is reduced. Uncertainities considered satisfy a generalized matching condition. We show that, high gain control laws can result in small tracking error of O(¿), where ¿ is a small design parameter. Furthermore, an alternate scheme based on the variable structure control strategy is presented which results in zero tracking error.