這篇論文提出了一系列基於描述形式的多項式模糊模型 (PFM) 最佳控制設計方法，旨在解決傳統模糊控制中保守性和設計靈活性不足的問題。這些方法的核心是將閉迴路系統結合模糊控制器，以平行分佈補償 (PDC) 的描述形式表示，從而使設計過程更加系統化和有效。第一種方法運用描述表示及共用的李雅普諾夫函數與多項式模糊鬆弛矩陣，達成降低保守性的效果。然而，由於多項式模糊鬆弛矩陣的應用，控制設計中出現雙模糊求和的挑戰。為此，論文中採用了共正定鬆弛方法來應對此問題，從而有效解決了設計過程中的複雜性。第二種方法聚焦於利用多重李雅普諾夫函數來實現更寬鬆的穩定性條件，這在系統動態複雜且非線性的情況下尤其重要，此方法將輸入約束納入考量，使控制設計更具實際適用性。論文還深入分析了在控制設計過程中考慮隸屬函數時間導數的必要性，以提高系統響應的準確性和穩定性。針對動力滑翔翼 (PPG) 的實際應用，第三種方法特別關注橫向控制設計，將輸入約束整合進設計中，以應對PPG飛行中的實際情況和限制。這一設計策略不僅提升了系統的可操作性，還確保了在不同飛行條件下的穩定性能。本論文的最終目標是透過這些控制設計方法，最小化給定目標函數的上限，以達成系統性能的優化。透過多個模擬實例，驗證了所提設計的可行性與有效性，這些實例充分證明了方法的理論合理性與實際應用的潛力。;This dissertation presents a series of optimum control design methodologies based on descriptor form for the polynomial fuzzy model (PFM). These methodologies begin by representing the closed-loop system of the PFM with a fuzzy controller, implemented using parallel distributed compensation (PDC) in descriptor form. The first methodology leverages the descriptor representation, employing a commonly used Lyapunov function and polynomial fuzzy slack matrices to achieve less conservative and more flexible results. The use of polynomial fuzzy slack matrices introduces the challenge of a double fuzzy summation issue in the control design. A copositive relaxation approach is adopted to address this complexity, effectively mitigating the issue. In the second methodology, a multiple Lyapunov function is utilized to obtain more relaxed conditions for stability analysis. This approach also incorporates input constraints into the optimum control design, addressing practical situations. By utilizing the multiple Lyapunov function, the time derivatives of membership functions are taken into account in the control design process. The third methodology focuses on lateral control for a powered paraglider (PPG) application, where input constraints are integrated to accommodate practical considerations specific to PPG. The overarching goal of these control design methodologies is to minimize the upper bound of a given objective function, thereby optimizing system performance. The validity of the proposed designs is demonstrated through a series of simulation examples, which confirm their theoretical soundness and showcase their potential for practical implementation.
