切換式靜態輸出回授控制—齊次李亞普諾夫法;Switching Static Output Feedback Controller for Polynomial Fuzzy Systems via Homogeneous Lyapunov Functions

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Title:	切換式靜態輸出回授控制—齊次李亞普諾夫法;Switching Static Output Feedback Controller for Polynomial Fuzzy Systems via Homogeneous Lyapunov Functions
Authors:	梁恩晟;Liang, En-Chen
Contributors:	機械工程學系
Keywords:	平方和(sum of squares);多項式模糊系統(polynomial fuzzy systems);尤拉齊次多項式定理(Euler′s Theorem for Homogeneous Functions);切換式靜態輸出回授控制(switching static output feedback control);最小型片段式李亞普諾夫函數(minimum-type piecewise Lyapunov functions);Sum of squares;Polynomial fuzzy systems;Euler′s Theorem for Homogeneous Functions;Switching static output feedback control;Minimum-type piecewise Lyapunov functions
Date:	2019-07-24
Issue Date:	2019-09-03 16:34:38 (UTC+8)
Publisher:	國立中央大學
Abstract:	本論文探討多項式模糊系統之切換式靜態輸出回授控制器設計，包含了連續時間系統及離散時間系統。藉由最小型片段式李亞普諾夫函數作穩定性分析，其型式為V(x)=\min_{1\leq l \leq N}\big\{V_l(x)\big\}，片段式李亞普諾夫函數亦為控制器切換的依據。在連續時間系統中，為了解決非凸項$\dot P(x)$的問題，使用尤拉齊次多項式定理來建立片段函數 V_l(x)=x^TP_l(x)x=\frac{1}{g(g-1)}x^T\nabla_{xx}V_l(x)x 在離散系統中，為了避免未知數的影響，以利電腦模擬順利進行，本論文將片段函數定義為V_l(x)=x^TP_l^{-1}(\tilde x)x，其中$\tilde x$是不受控制力直接影響的狀態集合，在文中有詳細說明。在電腦模擬中，使用了平方和方法檢測穩定性條件，並設計出切換式靜態輸出回授控制器。;In this paper, we study switching static output feedback control problem for both continuous- and discrete-time polynomial fuzzy systems. The stabilization of the systems is proved with minimum-type piecewise Lyapunov functions, which have the form V(x)=\min_{1\leq l \leq N}\big\{V_l(x)\big\}. Switching mechanism of the controllers is also based on piecewise Lyapunov functions. In continuous-time systems, in order to remove non-convex term \dot P(x), via Euler′s theorem for homogeneous functions we establish piecewise functions as follows. V_l(x)=x^TP_l(x)x=\frac{1}{g(g-1)}x^T\nabla_{xx}V_l(x)x In discrete-time systems, the piecewise functions are defined as V_l(x)=x^TP_l^{-1}(\tilde x)x$ to prevent problems where \tilde x is the set of states whose corresponding row in B_i(x) are empty. Further details are described in the text. In numerical examples, stability conditions and controller synthesis are tested and solved via sum-of-squares approach.
Appears in Collections:	[Graduate Institute of Mechanical Engineering] Electronic Thesis & Dissertation

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