Design and analysis of a new adaptive robust control scheme for a class of nonlinear uncertain systems

Abstract

This paper presents a new adaptive robust control scheme which is the extension of (Xu et al ., 1997) in the sense that more general classes of nonlinear uncertain dynamical systems are under consideration. To reduce the robust control gain and widen the application scope of adaptive techniques, the system uncertainties are classified into two different categories: the structured and non-structured uncertainties. The structured uncertainty is estimated with adaptation and compensated. Meanwhile, the adaptive robust method is applied to deal with the non-structured uncertainty by estimating unknown parameters in the upper bounding function. The μ-modification scheme is used to cease parameter adaptation in accordance with the adaptive robust control law. The new control scheme guarantees the uniform boundedness of the system and at the same time, the tracking error enters an arbitrarily designated zone in a finite time. The new control scheme also improves the result of (Xu et al ., 1997) in that the unknown input distribution matrix of the system can be state-dependent instead of being a constant matrix.