Global Adaptive Control for Uncertain Nonlinear Systems under Non-Lipschitz Condition with Quantized States

Abstract

A novel adaptive control method is designed for the uncertain nonlinear systems with quantized states under the condition that system nonlinearities do not satisfy the Lipschitz condition. In this paper, the global control for an uncertain nonlinear system with quantized states in the case that the system nonlinearities do not satisfy the Lipschitz condition is first achieved. Separation theorem is used to model the uncertainties appropriately and then an adaptive term is designed to help attenuate the effects of system uncertainties. Furthermore, the global boundedness of all signals of the closed-loop system is proved based on the Lyapunov stability theorem. Finally, simulation results are given to demonstrate the effectiveness of the proposed methods.