Study On Fuzzy Variable Structure Control Of Uncertain Nonlinear Systems

As an important branch in the field of intelligent control, fuzzy model based robust adaptive sliding-mode control for nonlinear systems has received more and more attention in recent years. Some correlative issues in this area are studied in this paper, such as the controller and observer design problem of uncertain nonlinear systems, which have the form of single-input-single-output (SISO) or multiple-input-multiple-output (MIMO). The design and analysis procedure is based on a series of control theories, including Lyapunov stability theory, adaptive control theory, decentralized control theory, sliding mode control theory, fuzzy approximate theory, and so on. The main work in this paper is summarized as follows.Firstly, using T-S fuzzy model as the approximator to a nonlinear system, the nonlinear system is described by the combination of local linear models. Based on Lyapunov theory, the variable structure controller is designed when uncertainties of every local linear model dissatisfy the matching condition. The closed-loop system is globally asymptotically stable and tracking error converges to zero.Secondly, a new design scheme of direct adaptive neural network controller for a class of unknown nonlinear systems is proposed. The design is based on the principle of sliding mode control and the approximation capability of RBF neural networks. Especially saturating function being instead of sign function in the supervisory controller, the closed-loop control systems is shown to be globally stable based on Lyapunov theory, with tracking error converging to zero.Thirdly, a new design scheme of direct adaptive neural network controller for a class of unknown nonlinear systems is proposed. The design is based on the principle of sliding mode control and the approximation capability of fuzzy logic systems. By introducing integral variable structure and adopting the adaptive compensation term of the approximation error, the closed-loop control systems is shown to be globally stable based on Lyapunov theory, with tracking error converging to zero.Lastly, a new design scheme of indirect adaptive fuzzy controller for a class of unknown nonlinear systems with unavailable system states is proposed. The design isbased on the principle of sliding mode control and the approximation capability of fuzzy logic systems. By introducing integral variable structure and high gain observer, the closed-loop control systems is shown to be globally stable in terms of Lyapunov theory, with tracking error converging to zero.Through the research in this paper, the design and analysis problems for several classes of uncertain nonlinear control systems have been properly solved. By making use of some effective methods including supervisory control, equivalent control, adaptive control, the schemes presented can guarantee the stability and tracking performance of the closed-loop control systems while the approximation error exists. Numerical simulation experiments of the control schemes demonstrate their effectiveness and practicability.