以LMI控制設計方法應用在離散時間非線性系統

大部分的控制理論都是針對連續時間的動態系統問題深入探討，但在實際的物理系統中還有許多系統是離散時間的模式，所以本論文就針對一些離散時間的非線性系統處理一些控制上的問題。我們利用適於非線性系統控制的T-S模糊模式(Takagi-Sugeno fuzzy model)，對非線性離散時間模式做T-S模糊模式化，而此模式化方式可近似或完整的表示原非線性系統。T-S模糊模式是近幾年來廣泛使用於處理非線性系統的控制方法之ㄧ，在設計控制器上使用所謂平行分佈補償(PDC)的概念，並利用線性系統的方法，最後將穩定性分析的問題轉為線性矩陣不等式(LMIs)的形式並利用數值方法去求解。我們研究的目的是利用此離散時間T-S模糊模式來設計控制器，並且處理一些模糊追蹤控制的問題。在追蹤控制上，我們藉由一些技巧把追蹤控制問題轉換成一個較為簡單處理的穩定性問題，然後先對狀態的可量測做探討。然而在現實情況中，系統的某些狀態可能不可得知，所以我們加入估測器以重建這些不可量測的狀態，當狀態不可量測時會產生一些誤差項，所以提出滿足Lipschitz-like Condition下的設計方法來解決上述問題。最後我們利用Matlab & Simulink對Hénon map和TCP/AQM系統來進行模擬，AQM（Active Queue Management主動式隊列管理）技術是基於路由器壅塞控制的關鍵技術，它和TCP端到端的壅塞控制相結合，是解決目前Internet壅塞控制問題的一個主要途徑。在TCP壅塞控制部份，我們並且使用NS-2 (Network Simulator) 來進行實驗。實驗結果顯示，在網路發生壅塞情況時，利用此離散時間T-S模糊控制器，確能獲得有效率的傳輸品質。

關鍵字

線性矩陣不等式；主動式佇列管理；模糊估測器；模糊追蹤控制；網際網路； T-S模糊模式

並列摘要

Tracking control design is an important issue for practical applications. Linear matrix inequalities (LMIs) based control design is proposed to deal with the output tracking problem for discrete-time nonlinear systems. Based on the capability of fuzzy systems approximating any nonlinear mapping, the discrete-time nonlinear systems are represented by the Takagi-Sugeno (TS) fuzzy models. As for the controller design, we use the concept of parallel distributed compensation (PDC) [1] to carry out these designs. For the purpose of tracking design, the new concepts of virtual desired variables and, in turn the so-called generalized kinematic constraints are introduced to simplify the design procedure. Based on these concepts, the design procedure is converted to a stabilization problem and the control gains are obtained by solving linear matrix inequalities. For immeasurable state variables, observer-based control design is proposed. For the most parts we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a Lipschitz-like property. Based on this setting, control gains and observer gains can be designed separately. Moreover, zero tracking error and estimation error are concluded. Finally, two di erent types of systems, Hénon map and TCP/AQM systems, are considered to demonstrate the design procedure.

並列關鍵字

internet ； linear matrix inequality (LMI) ； fuzzy tracking control ； Active queue management (AQM) ； fuzzy observer ； T-S fuzzy

參考文獻

n, "Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model," in Proc. FUZZ-IEEE'95, Yokohama, Japan, pp. 531-538, Mar. 1995.

[2] K. Tanaka, T. Ikeda, and H.O. Wang, "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H_infinte control theory, and linear matrix inequalities", IEEE Trans. Fuzzy Syst., vol. 4, pp. 1-13, 1996.

[3] B. S. Chen, C. S. Tseng, and H. J. Uang, "Mixed H2/H_infinte fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach", IEEE Trans. Fuzzy Syst., vol. 8, pp. 249-265, 2000.

[6] S. Floyd, and V. Jacobson, "Random Early Detection Gateways for Congestion Avoidance", IEEE/ACM Transactions on Networking, Vol. 1, No. 4, August 1993.

[7] S. Athuraliya, S.H. Low, V. H. Li, and Q. Yin, "REM: Active Queue Management", IEEE Network Magazine, Vol. 15, No. 3, May/June 2001.

國際替代計量

以LMI控制設計方法應用在離散時間非線性系統

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