複雜動態網路系統之同步化分析與設計

Synchronization Analysis and Design of Complex Dynamical Networks

黃國恩(Kuo-En Huang)

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/cycu200900997

摘要

本研究論文針對非線性複雜動態網路系統提出以LMI為基礎之同步化控制理論，並使用於不同型態的大型複雜連結網路中以達到同步化的目標。首先，將非線性複雜動態網路系統拆解成數個線性子系統，再融合T-S模糊規則將所有子系統精確的表示出原本非線性系統。針對此精確模糊受控系統，並根據平行分散式補償器 (PDC) 的概念設計同步化控制器，且利用Lyapunov穩定性分析方法找出系統同步化之充分條件，將充分條件轉換成線性矩陣不等式之型式，輔以強而有力的數值工具獲得同步化耦合增益。吾人利用推導出來的同步化理論，開始探討對於非線性系統在複雜動態網路同步化問題，並且建構出四種不同型態的網路，其中包含規則、小世界、隨機和無尺刻度網路模型，來深入探討網路連結結構對於連續與離散時間系統同步性質的影響。在數值模擬方面，吾人使以著名之連續與離散混沌系統做為驗證理論所推得結果。而由數值模擬呈現出令人滿意的結果可得知，本論文所提出之同步化方法是有效並可實行的。最後並針對這些不同的網路特徵與同步化特性做更近一步探討與比較。

關鍵字

T-S 模糊模型 ； 同步化 ； 線性矩陣不等式 ； 複雜網路 ； 耦合動態系統

並列摘要

This research proposes a brand new T-S fuzzy model-based approach to achieve syn-
chronization of complex coupled dynamical systems. The T-S fuzzy models are given to
exactly represent the complex coupled dynamical systems. Then the model-based fuzzy
synchronization design is carried out for each subsystem utilizing the concept of parallel
distributed compensation (PDC). We analyze the stability of the overall fuzzy synchro-
nization system by applying Lyapunov stability theory and derive stability conditions
by solving linear matrix inequalities (LMI) problem. The methodology has been applied
to both continuous-time and discrete-time complex networks, which consist of regular,
small-world, random, or scale-free networks. Three well-known examples, Chua's cir-
cuit and the driven pendulum for continuous-time and H enon map for discrete-time, are
considered as the coupled dynamical systems for the demonstration. Several numerical
simulations for the synchronization of these coupled dynamical systems illustrate the
e ectiveness of the proposed scheme. Finally, for complex networks with large nodes,
several interesting characteristics related to syntonization are revealed.

並列關鍵字

coupled dynamical systems ； synchronization ； linear matrix inequalities ； T-S fuzzy model ； complex networks

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