H-infinity 控制法則研究:串散射矩陣描述法

Abstract

本論文採用串散射矩陣描述法，將四種不同類別的H-infinity控制問題之求解方法統一化。文中顯示，這些不同的求解方法均可轉換成簡單的網路架構，因此較為容易處理。第一和第二種解法分別是針對線性連續時間和線性離散時間的H-infinity控制問題。就這兩種方法而言，結果顯示眾所周知的Glover-Doyle法則可用( J,J’)-無損分解和串散射矩陣描述法來表示，並能得到不同控制器間之相似轉換特性。第三種解法是用來解非線性仿射的 H-infinity 控制問題，就Hamiltonian系統的特性，我們定義了非線性的共軛( J,J’)-無損和共軛( -J,-J’)損系統，然後，運用網路理論來解此問題。最後本文討論奇異非線性 H-infinity 控制問題的解法，我們首先對擴增受控體引入一個虛擬的輸入訊號，這一步驟將奇異非線性 H-infinity 控制問題轉換成近似標準化的非線性仿射 控制問題，因此，可採用如同解標準化 H-infinity 控制問題一樣的方式來處理這個問題。

In this dissertation, a chain-scattering matrix description approach is utilized to unify the solving processes for four various classes of the H-infinity control problems. It is shown that these solving processes can be transformed into a simple lossless network which is easy to deal with in a network-theory context. The first and second solving processes are for the linear continuous- and discrete-time H-infinity control problems, respectively. For these processes, we show that the well-known Glover-Doyle algorithm can be formulated by using the (J,J')-lossless factorization and chain-scattering matrix description. Furthermore, the similarity transformation among H-infinity controllers are obtained. The nonlinear affine H-infinity control problem is considered as the third solving process. For this process, from the properties of Hamiltonian systems, we define the nonlinear conjugate (J,J')-lossless and conjugate (J,J')-expansive systems, and then this problem is formulated in terms of the chain-scattering matrix description and is solved by the classical network theory. Finally, the solving process for the singular nonlinear H-infinity control problem is examined. We first add an extra input signal into the augmented plant, which transforms this problem into a nearby nonsingular one, then can be solved as a standard nonlinear H-infinity control problem.