多項式模糊雙線性系統控制器設計—齊次李亞普諾夫法;Controller Design for Polynomial Fuzzy Bilinear Systems via Homogeneous Lyapunov Methods

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Title:	多項式模糊雙線性系統控制器設計—齊次李亞普諾夫法;Controller Design for Polynomial Fuzzy Bilinear Systems via Homogeneous Lyapunov Methods
Authors:	邱价偉;Chiu, Chieh-wei
Contributors:	機械工程學系
Keywords:	雙線性模糊系統;平方和;狀態回授控制;尤拉齊次多項式定理;bilinear fuzzy systems;sum of squares;state feedback;Euler′s Theorem for Homogeneous Function
Date:	2019-07-17
Issue Date:	2019-09-03 16:32:23 (UTC+8)
Publisher:	國立中央大學
Abstract:	本論文主要是研究多項式模糊雙線性系統之狀態回授控制器設計，以泰勒級數建模得出模糊系統，並且使用齊次多項式李亞普諾夫函數(Lyapunov function)及其對時間變化率推導穩定條件，本論文將以兩種方法解決雙線性系統問題，第一種方法我們將雙線性項Nxu與Bu合併成一項，第二種控制方法我們以三角函數來描述。其中在連續系統中利用尤拉齊次多項式解決$V(x)$對時間微分所造成V(x)問題並建立齊次之李亞普諾夫函數，而離散系統中則使用非齊次之李亞普諾夫函數，其中系統向量x中不受控制力影響的系統狀態集合而成，即需假設系統為可控典型式(canonical controllable form)，此限制才能使後續電腦模擬可行，內文將詳細說明。最後藉由電腦程式以平方和方法(Sum Of Squares)來檢驗模糊系統的穩定條件，並設計狀態回授控制器。;The main contribution in this thesis is a state feedback controller design for polynomial fuzzy bilinear systems modeled by Taylor series. The stability is proved with homogeneous polynomial Lyapunov function. In this thesis, two methods to tackle the control problem of polynomial fuzzy bilinear systems are proposed. In the first method we combine the bilinear term Nxu into the Bu term. The second method is to describe control input with trigonometric functions. For continuous-time systems, we utilize the Euler′s homogeneous polynomial theorem to solve the V(x) which is created by time derivative of V(x), and build the homogeneous Lyapunov function.In discrete-time systems, the non-homogeneous Lyapunov function state x is a collection of system states that are unaffected by control. This restriction is to avoid problems when doing simulation. The details will be described in this thesis. Finally in numerical simulations, we test the stability condition of the fuzzy systems via Sum Of Squares, and design the state feedback controllers.
Appears in Collections:	[Graduate Institute of Mechanical Engineering] Electronic Thesis & Dissertation

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