模糊大型系統之穩定及成本控制研究

The Study on Stabilization and Cost Control for Large-Scale Fuzzy Systems

林維偉(Wei-Wei Lin)

指導教授 ： 王文俊

國立中央大學/資訊電機學院/電機工程學系/博士(2007年)

摘要

本篇論文解決大型線性系統分散式穩定與成本控制問題。其中，大型系統是由數個子系統所結合而成，並且利用Takagi-Sugeno (T-S)模糊模型來表示。而兩個子系統互相連結的方式是以線性連結或是滿足相稱的非線性項連結。本文中，係利用平行分配補償(Parallel Distributed Compensation)來設計分散式糊模控制器。本文的主要貢獻有 (一)利用李亞普諾夫(Lyapunov)法則及瑞卡地(Riccate)不等式，提出對於模糊大型系統的穩定條件，並且滿足系統的相稱非線性連結限制。 (二)對於以線性連結的T-S模糊大型系統，提出兩個穩定條件。第一種條件是利用兩條不等式去滿足每個子系統，使整個大型系統漸近穩定。第二種條件是利用一個大型負定矩陣，一次就滿足整個大型系統漸近穩定；而大型矩陣當中包含了每個子系統與子系統的互相連結項。 (三)對於模糊大型系統的成本控制與穩定條件，我們也將討論，並且提出充分條件同時達成以上兩項目的。 (四)每一章所提出的控制方法或條件，我們都將以數值的例子或實際例子，利用線性矩陣不等式(Linear Matrix Inequality)求解，來實現並驗證其效能。

關鍵字

穩定條件 ； 模糊大型系統 ； 成本控制 ； 線性矩陣不等式

並列摘要

This dissertation studies the stabilization and decentralized guaranteed cost control problem for a large-scale system. The considered large-scale system is composed of several number of subsystems and each subsystem is represented by a Takagi-Sugeno (T-S) fuzzy model. The interconnection between any two subsystems may be linear or nonlinear with satisfies some matching condition. In each chapter, the decentralized fuzzy control by the concept of parallel distributed compensation (PDC) for each subsystem is synthesized. Based on Lyapunov criterion, some sufficient conditions are derived and the common and local state feedback gain are solved by linear matrix inequalities (LMIs) so that the whole closed-loop large-scale fuzzy system with the synthesized fuzzy control is asymptotically stable and cost control is guaranteed, respectively. In each chapter, a numerical or practical example is given to illustrate the control synthesis and its effectiveness.

並列關鍵字

Large-Scale Fuzzy System ； Cost Control ； Linear Matrix Inequalities ； Stabilization Conditions

參考文獻

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