A Class Of Uncertain Nonlinear System Adaptive Robust H_ ¡Þ Control

Uncertain nonlinear systems control is an important topic in control theory. Because of the complexity, the control problem of nonlinear system is always difficult. For uncertain nonlinear systems, the adaptive control method is applied to the robust control in this thesis. The controllers are designed respectively to guarantee the robust performances for the robust stabilization problem of time delay systems, H∞ output feedback control problem and the robust H∞ control problem of time delay systems. The main work and research results of this thesis is as the following:(1) The adaptive robust stabilization problem for a class of nonlinear systems with multiple time delays state disturbance is discussed. Under the situation that the upper bound of the time delay state disturbance is unknown but the time delay state disturbance satisfies certain match conditions, an adaptive robust stabilization controller is designed. Based on the Lyapunov-Krasovskii function, it is proved that the closed-loop system is indeed stable in the sense of uniform ultimate boundedness.(2) For a class of nonlinear systems with parametric uncertainties and external disturbance, the adaptive robust H∞ output feedback control problems are discussed under two uncertain situations. The sufficient conditions for the solvability of the control problem and the output feedback controller are obtained on the basis of Hamilton-Jacobi inequality.(3) For a class of nonlinear systems with time delay uncertainties and external disturbance, the parameter projection method of adaptive control is applied to nonlinear robust H∞ control. Using the adaptive law is proposed to estimate the upper bound of time delay uncertainties, and an adaptive robust H∞ controller is obtained.Presently, the research on nonlinear adaptive robust control is less. The state feedback control is always adopted, the output feedback control is not considered. And the robust stabilization problem, robust H∞ control problem for nonlinear systems with time delay state disturbance is waiting to be studied. We design adaptive robust controllers to solve these problems. Finally, the thesis is summarized and some content awaiting to be studied further is presented.