混合對角Lyapunov函數於T-S模糊控制之研究

T-S Fuzzy Control Using Normal-Mixed-Diagonal Lyapunov Functions

林蔚(Wei Lin)

指導教授 ： 練光祐 ； 張政元

中原大學/工學院/電機工程研究所/碩士(2009年)

https://doi.org/10.6840/cycu200900403

摘要

在控制系統中Lyapunov方法是一個非常強有力的分析和設計方式。相對比較於其它可能的Lyapunov 函數，對角類型Lyaunov函數具有更為簡單的形式及在許多範例中都顯示它賦有極大的優點。它較為眾人所知的是在處理Lotka-Volterra生態系統。在這篇論文中，我們發展出結合典型的Lyapunov函數及對角型式的Lyapunov函數的技巧來處理T-S模糊控制的問題。這個混合函數此後將稱為混合對角(NMD) Lyapunov函數。藉助這種方法，我們得到一組由線性矩陣不平等式(LMIs)組成的條件,可以同時用來確認系統穩定性及決定控制增益。研究過程中且嘗試以扇形條件放寛固式LMIs條件的保守性。最後，使用幾個數值例子來顯示我們所提出的方法的優點。並且如預期般發現NMD Lyapunov函數能應用在一些典型的模糊的函數並不適用的控制系統

關鍵字

對角混合Lyapunov函數 ； 對角Lyapunov函數 ； T-S模糊控制 ； 線性矩陣不等式

並列摘要

The Lyapunov approach is a very powerful method for the analysis and design in control systems. Compared to other possible Lyapunov functions, the diagonal-type Lyaunov functions is with simpler form and shows its great advantage in many instances. It is especially well known in dealing with Lotka-Volterra ecosystem. In this thesis, we develop the technique of combining the typical Lyapunov function and the diagonal-type Lyapunove function to deal with the T-S fuzzy control problems. The combined functions will be called normal-mixed-diagonal (NMD) Lyapunov functions. Using this approach, we obtain a set of linear matrix inequalities (LMIs) to confirm the system stability and determine the control gains as well. The attempt to relax the conserve LMIs due to sector conditions is also emphasized. Finally, several numerical examples are used to demonstrate the merits of the proposed method. We show that the NMD Lyapunov function works for some control systems whereas the typical fuzzy approach fails to be applied.

並列關鍵字

Diagonal-type Lyapunov ； HASH(0x9635e44) ； normal-mixed-diagonal(NMD) Lyapunov

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