Adaptive Fuzzy Control For Multivariable Nonlinear Continuous Systems

Firstly, based on a modified Lyapunov function and the approximation capability of the first type fuzzy systems, two new design schemes of decentralized adaptive fuzzy controller for two class of similar multivariable nonlinear continuous systems with a triangular matrix function control structure is proposed in this paper, respectively. The schemes employ a recursive algorithm to design controllers for every subsystem, respectively, and take predesigned control inputs as disturbances. By using Lyapunov method, the state of the closed-loop control system is proved to be bounded, with tracking error converging to zero.Secondly, based on the approximation capability of the second type fuzzy systems, two schemes of decentralized adaptive fuzzy controller for the above two kinds of multivariable systems are proposed in this paper, respectively. The state of the closed-loop control system is proved to be bounded with tracking error converging to zero.Finally, two schemes of fuzzy controller for a class of multi-joint robot manipulators are proposed in this paper. One scheme utilizes the approximation capability of the second type fuzzy systems to design controller. The design scheme is based on Lyapunov second method. The state of closed-loop control system is proved to be bounded with tracking error converging to zero. Another scheme integrates Genetic Algorithm to design adaptive fuzzy controller. A supervisory controller is used to ensure the state of the closed-loop control system bounded, and then Genetic Algorithm is used to adjust the parameters of the fuzzy system so that they can converge to the best values in probability meaning.By the research in this paper, the problems of fuzzy control for the above multivariable nonlinear continuous systems have been properly solved. The schemes presented can guarantee the global stable of the closed-loop control systems with tracking errors converging to zero, while the modeling errors exist. They can improve the performance of the closed-loop control systems and their robustness.