The Research For The Stability And Robust Control Theory Of Nonlinear Dynamic Systems

Along with the development of science and technology, the system object or process become larger and more complex in structure and scale than ever. Therefore, it is hard to get the accurate mathematic model of the system. In this way, it is very important to research the uncertain nonlinear dynamic systems for the purpose of theory significance and practical needs. This paper mainly deals with the study of stability and robust control for several kinds of nonlinear dynamic systems. Our research work mainly boils down to the following three parts: firstly, we discuss the stability of nonlinear dynamic neural network systems, and then, we work on the problem of trajectory tracking robust control for nonlinear rigid robot systems, finally, we discuss the problem of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot system. The content of this paper can be listed as following three parts.The first part mainly deals with the study of stability for nonlinear dynamic neural network systems. At first, we brief introduce the history of neural networks and the research progress of stability theory, and then, we examine the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Based on the Lyapunov-Krasovskii stability method, we originally give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Secondly, we analyze the global robust stability of delayed neural networks with discontinuous activation functions and normal-bounded uncertainties, and give the conditions of the global robust stability of systems in terms of a linear matrix inequality. After that, based on the linear matrix inequality technology and Filippov theory, we give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Finally, we introduce the models and applications of neural networks in robotic compensated control.The second part mainly deals with the study of trajectory tracking robust control for nonlinear rigid robot systems. At first, we briefly tell the history of rigid robotic systems, and then, introduce in detail the research progress of trajectory tracking control problems about nonlinear rigid robot systems and the application of intelligent control theory in robotic systems. Secondly, the dynamics model and its characteristics of rigid robotic system are introduced respectively, and then, we introduce some important mathematical concepts and definitions. Thirdly, we address the problem of robust tracking control using a PD-plus-feedforward controller and an intelligent adaptive robust compensator for a rigid robotic manipulator with uncertain dynamics and external disturbances. In this way, chattering can be effectively eliminated and asymptotic error convergence can be guaranteed. After that, A novel robust H_∞intelligent control strategy is proposed for the trajectory following problem of robot manipulators. The proposed system is comprised of a computed torque controller and neural robust controller. Based on Lyapunov stability theorem, it is shown that the proposed controller can guarantee H_∞tracking performance of robotic system in the sense that all variables of the closed-loop system are bounded. Finally, the problem of the robust tracking for a class of uncertain robotic systems with delays is investigated. A neural network system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. Based on the Lyapunov method and the linear matrix inequality approach, several sufficient conditions, which guarantee the robust stability of closed error systems, are derived.The third part mainly deals with the study of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot systems. Firstly, we introduce in detail the research progress of trajectory tracking control problems about nonlinear mobile robot systems and the application of intelligent control theory in mobile robotic systems. Secondly, the kinematics and dynamics model and its characteristics of mobile robotic system are introduced. After that, we propose a stable tracking control rule for nonholonomic mobile robot with completely unknown robot dynamics and unmodeled disturbance. A control strategy that integrate a kinematic controller and a adaptive wavelet neural network controller for nonholonomic mobile robots is presented. The adaptive wavelet neural network control system adopts a wavelet neural network with accurate approximation capability to represent the unknown dynamics of the nonholonomic mobile robot. It also uses a robust term to confront the inevitable approximation errors due to the finite number of wavelet bases functions and to disturbances. The tracking stability of the closed loop system, the convergence of the wavelet neural network weight-updating process and boundedness of wavelet neural network weight estimation errors are all guaranteed.Finally, the main innovations of the thesis are summarized, and the fields for further research are expected.