針對以Takagi-Sugeno模糊器處理非線性控制問題，本論文提出數個創新的方法以改善現有設計方式的缺點，並細分為兩個方向來探討：(i)以傳統平行分配補償(Parallel Distribution Compensation)的設計方式，(ii) 以區域為基礎之控制架構。首先，針對PDC控制架構，本論文結合協方差控制之方法，藉由給定共同正定矩陣後反向求解里阿柏諾方程組，以取得模糊控制器，不過，現有的設計方式在設計靜態輸出迴授模糊控制器時，大多需要外加限制條件而導致設計結果太過保守，因此本論文結合基因演算法與線性矩陣不等式求解器，提出新的演算法來解決此問題，其優點在於設計過程簡單，且不需要外加任何的限制條件或假設，所以設計結果更加寬鬆，不過當非線性系統的複雜度增加，會導致模糊控制器的規則數增加時，此時以PDC控制架構的控制器製作成本將大幅提高(大量模糊規則在解模糊計算必須以高速的硬體來完成)，在設計上也更加複雜而提高無解的發生率，因此進一步提出模糊區域控制架構，並推導其穩定條件與設計方法，該控制架構不但能降低設計的複雜度而且設計結果也能夠以簡單的硬體來實現，由模擬結果可知，既使控制器規則數大量簡化，模糊區域控制架構仍然能提供如同PDC控制架構一般的性能，最後將上述的研究成果套用到單一模糊區域求解靜態輸出迴授增益，說明該方法也可解決多頂點模型(polytopic model)的靜態輸出迴授強健控制問題，以上所提出的方法都經由數值模擬的方式，以驗證其正確性與可行性。

In this dissertation, several novel Takagi-Sugeno (T-S) fuzzy control approaches are developed for nonlinear control problems. These design approaches can be separated into two parts: (i) Parallel Distribution Compensation (PDC) design and (ii) Fuzzy Region Compensation (FRC) one.
The first type of T-S fuzzy control approach is developed for single input fuzzy control systems, in which all sub-models are represented as a controllability canonical form. The controller structure is based on the PDC control structure and the synthesis is derived from the covariance control techniques. Unfortunately, these state feedback designs are very difficult to deal with the static output feedback fuzzy control problems because the extra constraints or assumptions have to be attached. To overcome this problem, this dissertation proposes the mixed GA/LMI algorithm, which combines a standard Genetic Algorithm (GA) with LMI solver.
Even if PDC-based design approaches are very popular and ripe, it still has the following serious disadvantages when the fuzzy controller involving many IF-THEN rules: (i) The design result is difficult to implement with some simple hardware or cheap microcontroller. (ii) The total number of Lyapunov stability conditions is rapidly increased. (iii) The modeling errors between a T-S fuzzy model and a nonlinear model could result in the instability or undesired performances when applying the T-S fuzzy controller to the nonlinear models.
To improve the above problems, the FRC control structure is developed in this dissertation. The design idea is to partition the fuzzy model into several regions, and each region is redefined as a polytopic model. In this dissertation, this kind of fuzzy model is named T-S fuzzy region model or TSFRM for short. The proposed fuzzy controller is called T-S fuzzy region controller (TSFRC), in which the controller rule has to stabilize the polytopic model of the fuzzy region and the original nonlinear model is asymptotically stable. The stability analysis and control synthesis are derived from Lyapunov stability criterion, which is considered the robust compensation and is expressed in terms of Linear Matrix Inequalities (LMIs). Comparing with PDC-based designs, TSFRC is easy to design and to implement with simple hardware or a cheap microcontroller. Even if the total number of controller rules of TSFRC is reduced, TSFRC is able to provide competent performances as well as PDC-based designs. By combining the region-based control structure and GA/LMI algorithm, we further shows that the proposed ideas in the field of T-S fuzzy control can be applied to design the static output feedback robust control problems.
It should be noted that the merit of this dissertation is to provide simple design procedures and realizable solutions for state and static output feedback designs when the original T-S fuzzy model is complicated. From the synthesis point of view, these design approaches can deal with various performance constraints without complex mathematical derivations. From the implementation point of view, the design results can be implemented with simple hardware or a cheap microcontroller.

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