Robust approximate control of time-varying uncertain nonlinear systems

We present an approach for control of a class of nonlinear systems with unknown, time-varying parameters or disturbances whose bounds are known, but are not required to enter linearly in the state equations. Control scheme is presented for nonlinear systems which fail to have a well defined relative degree, minimum phase property, and feedback linearizability condition. Therefore, this scheme is applicable to a wide class of nonlinear systems. By a Taylor series of the system about the nominal parameter vector coupled with the approximate feedback linearization concepts and subject to a structure matching condition, it is proved that the presented control law leads to an asymptotically stable closed loop system with bounds on tracking error. Also, when the nonlinear system has a well defined relative degree and is minimum phase on its operating range, the tracking error converges exponentially to zero. Furthermore, we present a parallel scheme for robust state regulation. It is proved that the regulation error converges exponentially to zero.