Practical stabilization of a class of nonlinear systems with partially known uncertainties

In this paper we deal with robust control of a class of nonlinear systems which contain uncertainties. It can be viewed as an extension of the work in Corless and Leitmann [IEEE Trans. Aurom. Conrrol, AC-Xi, 1139-1144 (1981)] for the cases where the vector of uncertainties is only partially known. To cope with the uncertainties, an adaptive controller using a dead-zone and a hysteresis function is proposed, and both the uniform boundedness of all the closed-loop signals and uniform ultimate boundedness of the system state are guaranteed. In contrast with some previous attempts to relax the a priori knowledge on the uncertainties bounds by using a discontinuous control law, we propose continuous control laws in this paper. Hence, chattering problems (which have practical importance) can be avoided.