Adaptive Fuzzy Control Of Observer-based Nonlinear Systems

As well known, if the state variables are immeasurable, the control strategies proposed via state feedback will be limited to be implemented in practice. Thus, the research of adaptive fuzzy backstepping control method via output feedback will become very significant. In terms of the existing adaptive fuzzy or neural network control design, the stability analysis of the observation error dynamics mostly depends on the solvability of a quadratic matrix inequality. However, there is not a common method to solve the quadratic matrix inequality. On the other hand, the quadratic matrix inequality is also very difficult to find a feasible solution. So the existing adaptive fuzzy or neural network output feedback control strategies are difficult to be applied in practice.In this thesis, a state observer is first designed to estimate the state of the system, and then a control scheme is developed by combining adaptive fuzzy control theorem, the Lyapunov stability theory with the backstepping technique. The stability condition of the dynamic observation error is given by using the solvability of a set of linear matrix inequality. Compared with the matrix inequality condition in the present results, the control scheme proposed by us is easily implemented in practice and less conservative. The specific research contents are as follows:First, observer-based adaptive fuzzy output feedback control is proposed for a class of single-input single-output strict feedback nonlinear systems. Then by combing the Lyapunov stability theory, adaptive fuzzy method with backstepping technique, adaptive fuzzy controller is designed.Second, adaptive fuzzy output feedback control strategy is proposed for a class of nonlinear systems with completely unknown interconnections. The proposed control method removes the assumption that the interconnection term is bounded by some known upper bound function. Apparently, the system under consideration is more of generality.Finally, summarize the obtained results on observer-based adaptive fuzzy control for nonlinear systems, and give the expectation of future research.