平方和模糊控制器設計-齊次多項式法

SOS-based Fuzzy Controller Design - Homogeneous Polynomial Approach

林雨澤(Yu-Tse Lin)

指導教授 ： 羅吉昌

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

本論文主要研究連續與離散模糊控制系統的非二次穩定
(non-quadratic stability) 條件，關於擴展狀態決定於高階的非二次李
亞普諾夫函數，其函數形式是V(x)= 1/2x′Q^−1(x)x，對於連續系統而
言，其李亞普諾夫函數V(x)對時間t 微分將會產生Q(x)之微分項，為了避免這個問題，將引用尤拉齊次多項式定理，並且使用建模技巧泰勒級數，再以平方和方法(sum of squares) 去檢驗其模糊系統之穩定性條件；對於離散系統而言，也引用尤拉齊次多項式定理，以平方和方法檢驗其模糊系統之穩定性條件。最後，模擬其多項式模糊系統，表現出本論文提出之方法是有效的。

關鍵字

非二次穩定 ； 平方和 ； 參數相依齊次多項式 ； 模糊系統 ； 尤拉齊次多項式定理 ； 泰勒級數

並列摘要

In this thesis,it is mainly to research the non-quadratic stability conditions of continuous and discrete-time fuzzy systems.Extension of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V (x) = 1/2x′Q−1(x)x.For the continuous case,it will
produce the derivative term of Q(x)from V(x) for differential t,in order to avoid this problem,we will reference Euler homogeneous polynomial theorem,using the theorem to detect its stability conditions of fuzzy systems,
and use the modeling techniques Taylor series,then test it with the method of sum of squares to determine the stability.For the discrete-time case,also reference Euler homogeneous polynomial theorem,determining the stability with the method of sum of squares.Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed method being effective.

並列關鍵字

Non-quadratic stability ； Sum of squares ； Homogeneous polynomially parameter-dependent functions ； T-S fuzzy systems ； Euler’s Theorem for Homogeneous Functions ； Taylor-Series

參考文獻

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