考慮二次成本函數之不定延遲奇異系統強健T-S模糊控制器設計

Robust T-S Fuzzy Controller Design for Uncertain Time-delay Singular Systems with Quadratic Cost Consideration

江明勳(Ming-Hsun Chiang)

指導教授 ： 曾傳蘆

國立臺北科技大學/機電學院/機電整合研究所/碩士(2005年)

摘要

本論文針對不定時間延遲奇異系統提出利用T-S模糊模型之強健T-S模糊控制器設計方法，可使局部線性閉迴路系統具有強健穩定性及最佳性能表現，並且由T-S模型的特性推廣至整個非線性系統皆有相同結果。
考慮一個二次成本函數的非線性時間延遲奇異系統，藉由T-S模糊模式的建立，將非線性系統與以局部線性化，並經由特別選定的李亞普諾夫泛函，將奇異系統予以一般化，再使用Schwarz 不等式的處理方法與李亞普諾夫定理，推導出不定時間延遲模糊控制系統之二次漸進穩定的條件，此條件可進一步轉換成線性矩陣不等式條件。此外，利用線性矩陣不等式(LMIs)的理論與技術，找出使系統具有較佳二次成本函數之線性矩陣不等式條件，進而處理二次成本函數最佳化問題。由以上穩定與最佳化之LMI條件。本論文推導出相關之設計方法，只要利用LMI工具程式解出一符合特定假設的實矩陣P與回授控制矩陣 ，則閉迴路不定性時間延遲模糊控制系統即可具有穩定性，且能保證其成本函數具有最小上界，達到實際強健控制的設計目的。至於動態輸出回授觀測器亦可以類似方式求得，而其問題之求解將轉換至解決線性矩陣不等式(LMIs)的問題，其最終等價條件為解決兩個線性矩陣不等式(LMIs)的問題。

關鍵字

奇異系統 ； 描述子系統 ； 成本函數 ； 不定系統 ； 時間延遲系統 ； T-S模糊模型 ； 模糊控制器 ； 李亞普諾夫穩定性 ； 線性矩陣不等式

並列摘要

This paper is to investigate the guaranteed cost control problem for a class of fuzzy uncertain singular time-delay systems. Based on the Tagaki-Sugeno fuzzy model and controller, the system can be locally linearlized. If we can find a special matrix which can transfer the singular problem into the normal system, then the associated robust stability condition is derived to ensure the robust quadratic stability of the system by using Lyapunov approach, and at the same time the upper bound of considered cost is found. In addition, the Linear Matrix Inequality (LMI) techniques are employed to solve the guaranteed cost problem. A fuzzy controller design algorithm is developed to stabilize the uncertain system and keep the cost at a certain level. Also, the method of finding observer-based dynamic output feedback controller is derived, and then the sufficient condition is transformed into a Linear Matrix Inequality (LMI) problem again. Observer-based control law can be obtained by solving two LMIs.

並列關鍵字

singular system ； descriptor system ； cost function ； uncertain system ； time-delay system ； fuzzy controller ； T-S fuzzy model ； Lyapunov stability ； linear matrix inequalities

參考文獻

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