Adaptive Fuzzy Control For Unmatched Uncertain Nonlinear Systems

With the developing of modern science and technology, many engineering control systems are becoming more complex. These systems have serious uncertainties, nonlinearity, multivariable properties, and tight coupling properties. Therefore, study on the control problem for complex uncertain nonlinear systems has great significance in theory and practical applications. Adaptive fuzzy control has been shown to be one of the most effective methods for the complex uncertain nonlinear systems. Based on the theoretical framework of fuzzy control, adaptive control and nonlinear robust control, and by using fuzzy logic systems to model the complex uncertain nonlinear systems, a series of adaptive fuzzy control methods and strategies are proposed, and the stability, the convergence and robustness of the closed-loop systems are proved by mathematical methods. The main research works in this doctoral dissertation are stated as follows:First, three adaptive fuzzy state-feedback control design methods are proposed for three classes unmatched single input and single output uncertain nonlinear systems with measurable states. These nonlinear systems contain unknown nonlinear functions, nonsmooth nonlinear inputs (saturations, dead-zones and hysteresis), unmodeled dynamics and stochastic disturbances. In the control design, fuzzy logic systems are used to identify the unknown nonlinear functions or combinational functions. By combining backstepping technique, adaptive robust control theory, stochastic small-gain theory, barrier Lyapunov function method, adaptive fuzzy control, three adaptive fuzzy control strategies are developed. The stability and convergence of the closed-loop systems are proved based on Lyapnuov stability theory and stochastic satiblity theory. The effectiveness of the proposed approaches are illustrated from simulation results.Second, three adaptive fuzzy output-feedback control design methods are proposed for three classes unmatched single input and single output uncertain nonlinear systems with immeasurable states. These nonlinear systems contain unmeasured states, unknown nonlinear functions, input saturations, dead-zones and unmodeled dynamics. Fuzzy logic systems are used to identify the unknown nonlinear functions, three fuzzy state observers are designed to estimate the unmeasured states, respectively. By combining backstepping technique, adaptive robust control theory, small-gain theory, adaptive fuzzy control technique and dynamic surface control technique, three adaptive fuzzy robust output feedback control strategies are developed. The stability and convergence of the closed-loop systems are proved based on Lyapnuov stability theory. The effectiveness of the proposed approaches are illustrated from simulation results.Third, two adaptive fuzzy output-feedback decentralized control design methods are proposed for two classes unmatched interconnected large-scale uncertain nonlinear systems with immeasurable states. The two nonlinear systems are nonlinear strict-feedback nonlinear systems and pure-feedback nonlinear system, respectively. By using Butterworth low-pass filter and coordinate transformation, the previous pure-feedback system can be transformed as strict-feedback systems. Fuzzy logic systems are used to identify the unknown nonlinear functions of the two strict-feedback systems, and fuzzy state observers and high gain fuzzy filter observers are designed to estimate the unmeasured states, respectively. By combining backstepping technique, decentralized control theory and dynamic surface control technique, two adaptive fuzzy output feedback decentralized control strategies are developed. The stability and convergence of the closed-loop systems are proved based on Lyapnuov stability theory and Lyapunov-Krasovskii functional theory. The effectiveness of the proposed approaches are illustrated from simulation results and comparison.Forth, two adaptive fuzzy output-feedback control design methods are proposed for two classes unmatched multi input and multi output uncertain nonlinear stochastic systems and time-delay systems with immeasurable states. These nonlinear systems contain unknown nonlinear functions, unknown dead-zones, unknown hysteresis, unknown control directions, unmodeled dynamics and stochastic disturbances. Two fuzzy state observers are designed to estimate the unmeasured states, respectively. Based on the observers, and by combining backstepping technique. Nussbaum gain technique and multi-variable decoupling technique, two adaptive fuzzy robust output feedback control strategies are developed. The stability and convergence of the closed-loop systems are proved based on Lyapnuov stability theory and stochastic stability theory. The effectiveness of the proposed approaches are illustrated from simulation results.