模糊系統觀測控制器設計─齊次多項式尤拉法;Observer and Controller Design of Fuzzy Systems via Homogeneous Euler′s Method

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Title:	模糊系統觀測控制器設計─齊次多項式尤拉法;Observer and Controller Design of Fuzzy Systems via Homogeneous Euler′s Method
Authors:	林承緯;Lin,Cheng-wei
Contributors:	機械工程學系
Keywords:	非二次穩定;平方和;參數相依齊次多項式;Takagi-Sugeno模糊系統;尤拉齊次多項式定理;泰勒級數;Non-quadratic stability;Sum of squares;Homogeneous polynomially parameter-dependent (HPPD) functions;T-S fuzzy systems;Euler′s Theorem for Homogeneous Functions;Taylor-Series
Date:	2015-07-30
Issue Date:	2015-09-23 15:12:42 (UTC+8)
Publisher:	國立中央大學
Abstract:	本論文主要研究連續模糊系統的非二次穩定(non-quadratic stability) 條件，以泰勒級數建模得出模糊系統，且以非二次的李亞普諾夫函數(Lyapunov function) 及對時間的變化率作為穩定的條件，對於決定擴展狀態的高階李亞普諾夫函數，其形式為 V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e] 而使用尤拉齊次多項式可以排除V(x,e)對時間t 微分所產生Q(x) 之微分項，再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條件，並設計出其觀測器及控制器。由於觀測器與控制器的相依性，分離設計並不容易，本論文將以限制條件分段解析，並找出有條件下的分離設計方法。;It′s not easy to separate the synthesis of observer and controller due to their dependability. The main contribution in this thesis is non-quadratic stability of continuous fuzzy systems, which is modeled by Taylor series method. And we can solve the inequations derived from non-quadratic Lyapunov function and its time gradient. The form of extension from the state dependent Riccati inequalities to non-quadratic Lyapunov function is V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e]. To overcome the di erential terms of Q(x) derived from time gradient of V(x,e), we introduce Euler′s homogeneous polynomial theorem to derive the SOS condition and solve for the observer and controller with sum-of-squares approach.
Appears in Collections:	[Graduate Institute of Mechanical Engineering] Electronic Thesis & Dissertation

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