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 the previous work of Xu et al. in the sense that more general classes of nonlinear uncertain dynamical systems are under consideration. To reduce the robust control gain and to 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 can be separated and expressed as the product of known functions of states and a set of unknown constants. The non-structured uncertainty to be addressed in this paper is distinct from that considered in the earlier work of Xu et al. in that its upper bounding function is only partially known with unknown parameters. Moreover, the bounding function is convex to the set of unknown parameters, that is the bounding function is no longer linear in parameters. 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 emploved previously by Xu et al. 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 earlier result of Xu et al. in that the unknown input distribution matrix of the system input can be state dependent, instead of being a constant matrix.