本論文探討如何將非線性系統精確表示成T-S模糊模型，並使用智慧型方法用以達成各種常見的控制目標，其間兼顧系統的穩定性、指數收斂性質、快速暫態響應、以及強健性等諸多性質的考量。首先，提出系統化方法，將非線性系統精確地表示成T-S模糊模型。利用這種方法，少量模糊的規則就足以在一定區域內完整無誤地表示此非線性系統。本論文中同時說明了，此過程中可將系統之不確定性全由歸屬函數加以刻畫描述，而子系統矩陣依然能保持恆定且已知。一個嶄新的控制想法於焉產生: 利用已知的系統矩陣用以求解滿足系統穩定性條件的固定回授增益；另一方面，以類神經網路調整模糊控制器的等級函數以獲取較快速的暫態響應。此處等級函數，乃源於控制規則的歸屬函數，是利用倒傳遞網路學習取得最佳的數值。至於穩定性條件則使用Lyapunov法求得，可保證閉迴路系統穩定無虞，此充分條件可轉換成線性矩陣不等式之型式，輔以強有力的數值工具獲得控制增益。
此論文另一重點乃介紹所謂虛擬預期變數綜合法來完成許多不同形式的T-S模糊系統控制目標之實現。控制目標的範圍從混沌控制 — (一)調節；(二)非線性模型追蹤；(三)輸出調節；(四)輸出跟蹤，到反控制問題 — (五) 混沌化，而目的在於達到零狀態誤差。這裡我們到很多物理系統的模糊集合的歸屬函數是滿足類Lipschitz的特性。實際上的虛擬預期變數綜合法的控制增益，是透過一組線性矩陣不等式求解所得到的，這線性矩陣不等式的形式與前述穩定問題的線性矩陣不等式形式相同。而且，為了提昇系統暫態之效能，結合虛擬預期變數綜合法與類神經網路來調整控制器的等級函數，做為最終的解決方案。
針對模糊系統暫態性能提昇之智慧型控制器設計方法，適合應用在許許多多的非線性系統。在數值模擬方面，我們使用幾個著名連續時間與離散時間的非線性系統為例，其中，結合類神經網路方法的模糊控制器，以球與樑的系統和拖車系統做為其應用的例子；而結合類神經網路方法的虛擬預期變數綜合控制器，則以Chua的電路和H'enon映射為應用的例子。

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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