| Summary: | 博士 === 國立臺灣科技大學 === 電子工程系 === 94 === This dissertation centers on the issue of representing nonlinear systems precisely as Takagi-Sugeno (T-S) fuzzy models and making use of intelligent method, so that various control objectives can be achieved. Meanwhile, system stability, exponential convergence property, improvement of transient response, and robustness are all taken into consideration. First, a method is given to systematically represent a nonlinear system exactly as a T-S fuzzy model. By the method, not only few fuzzy rules are enough to represent the nonlinear system precisely. Besides, the derived fuzzy model gives zero modeling errors in the universe of discourse where the fuzzy sets are defined. As the overall inferred output is presented, the method mentioned above is illustrated to put all the system uncertainty into the membership functions, whereas the local system matrices are kept constant and known. Thereby, a brand new concept about control design is acquired. We can make use of the known existing system matrices to obtain the controller gains to satisfy the conditions of system stability. Moreover, by using neural networks to tune control grade functions, a new control scheme is proposed to improve the system performance of the transient response of fuzzy systems. The grade functions, resulting from the membership functions of the control rules, are the optimization achieved by a back-propagation network (BPN). Using Lyapunov's direct method, the stability analysis is performed well on the overall closed-loop system. It derives the sufficient conditions which, as a result, are formulated into linear matrix inequalities (LMIs). Next, using powerful numerical toolboxes, the linear matrix inequalities are solved and controller gains are obtained.
With regards to another emphasis in the dissertation, the new concepts, virtual-desired-variables synthesis and generalized kinematic constraints, are introduced to benefit the various control objectives design. The control objectives range from the chaotic control - i) regulation; ii) nonlinear model following; iii) output regulation; and iv) output tracking, to the anticontrol issue - v) chaotification. Meanwhile, zero tracking error is concluded. Here we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a Lipschitz-like property. The control gains of virtual-desired-variables synthesis are determined by solving a set of LMIs, the same type of LMIs for stabilization problem. Moreover, to improve the system's performance, a new scheme combining virtual-desired-variables synthesis and tuning algorithms by neural networks is proposed to be the ultimate solution.
The proposed intelligent methods can achieve high performance for both continuous and discrete-time fuzzy systems. They can be applied to many nonlinear systems. Here, the fuzzy controller using neural networks method is applied to the numerical simulations of several well-known nonlinear systems, such as ball-and-beam system and truck-trailer system. Besides, virtual-desired-variables synthesis using neural networks method is applied to the numerical simulations of Chua's circuit and H'enon map.
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