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Practical stabilization of a class of nonlinear systems with partially known uncertainties. (English) Zbl 0825.93650
Summary: 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 [M. J. Corless and G. Leitmann, IEEE Trans. Autom. Control 26, 1139–1144 (1981; Zbl 0473.93056)] 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.

MSC:
93D21 Adaptive or robust stabilization
93B51 Design techniques (robust design, computer-aided design, etc.)
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93D30 Lyapunov and storage functions
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