不定性大型系統之分散式強健控制器與觀察器設計

Abstract

在系統參數變動下，確保閉迴路系統的穩定性為典型控制設計問題的首要 考量。且隨著現代工業技術的需求，系統所考慮的範圍與結構在規劃､設 計及體現上變得更為寬廣與複雜。本論文嘗試以時域的觀點從事不定性大 型系統的分散式控制理論推導。本論文使用匹配的觀念與李楷悌方程法， 達成一般化不定性大型系統的分散式強健控制器與觀察器設計。將藕連矩 陣與不定項適當的分解，可使匹配部份以回授控制或觀察器增益克服；並 造成非匹配部份只需滿足一些簡單的限制就能保證系統穩定性的建立及系 統狀態的測得。所提出方法優於現存方法的顯著特徵在於能容易地處理非 線性參數變動的問題。本論文亦經由二次分散式穩定問題的分析，嘗試建 立強健控制理論中兩個主要研究方法 -- 時域方法與頻域方法間的關係。 藉由一組代數李楷悌方程式的求解，二次分散式穩定問題得以完全解決； 且其與H-無限控制理論間的相關性亦可獲得。本論文亦利用分散式控制理 論探討大型系統干擾衰減的問題。面對給定的衰減水平要求，所提出的法 則是藉由一組代數李楷悌方程式的求解而達成 所需的H.inf.區域狀態回 授控制器設計。同時在所有的系統狀態均能獲得的前題下，推論出造成閉 迴路轉移函數最小 H.inf.模的分散式控制器僅需為非動態狀態回授。 The objective of this dissertation is to provide a comprehensive decentralized control theory from time domain point of view for uncertain large-scale systems. The concept of matched conditions and Riccati equation approach are used to obtain decentralized observers and/or decentralized stabilizing control laws. The interconnection matrices and the uncertainties of the system are decomposed into matched and mismatched portions. It is well known that the matched portion can be neutralized by high gain feedback. The objective of the decomposition is by imposing only some simple restrictions on the mismatched portion while using observer dynamic and feedback control to compensate the matched component such that the true states can be estimated and the stability of the overall system can be guaranteed. A distinguishing feature of the proposed technique is that it solves nonlinear parameter variation problems easily. To establish relations between two major research directions in decentralized robust control theory: the frequency domain approach involving input-output models and H.inf. tools and the time domain approach using Lyapunov functions and state space models, the problem of quadratically decentralized stabilization is attacked. It is shown that the complete solution to the quadratically decentralized stabilizability problem is equivalent to solve a set of algebraic Riccati equations containing some free parameters. And relations between robust stabilizability problem and H.inf. control theory are established. The problem of disturbances attenuation in large-scale systems by decentralized control is also investigated. A new technique is developed for constructing H.inf. local state feedback controls by iteratively solving a set of algebraic Riccati equations. Besides, once all the states arel available, one can come as close as desired to the infimal norm of the closed-loop transfer function through all decentralized controls by using nondynamic local state