本篇論文探討一個非線性隨機耦合網路的強健同步化問題。針對一個透過卜瓦松過程耦合下的非線性隨機耦合網路，我們探討了漸進同步化與強健同步化的特性。對於漸進同步化與為了能有效抑制外部雜訊的強健同步化探討，各自所對應的Hamilton-Jacobi不等式條件將被提出。然而，針對Hamilton-Jacobi不等式直接求解有技術上的困難；因此，本篇提出了Takagi-Sugeno模糊系統使線性動態系統近似非線性動態系統從而簡化對Hamilton-Jacobi不等式求解的難度。由於Takagi-Sugeno模糊系統的提出，Hamilton-Jacobi不等式可被轉換為線性矩陣不等式。藉由Matlab的LMI-toolbox的使用，漸進同步化與強健同步化的條件將能較簡單地被驗正。隨後，對於一個透過卜瓦松過程耦合下的非線性隨機耦合網路，本篇提出了一個在不失漸進同步化與強健同步化的特性下，刪減多餘的耦合來達到最小耦合設計。與此同時，結合線性矩陣不等式本篇提出了一個判斷準則來找尋多餘且可被移除的耦合。藉由該判斷準則，一個簡易的最小耦合設計流程將被建立。文末，最小耦合設計將應用於十個羅倫斯震盪器所形成的非線性隨機耦合網路。經由最小耦合設計流程建構出一個不失漸進同步化與強健同步化的最小耦合網路。

In this paper, we discuss a robust synchronization problem for nonlinear stochastic coupling networks through Poisson diffusions. In the robust synchronization problem, we study the asymptotical synchronizability in probability of the nonlinear stochastic coupling networks through Poisson diffusion via a Hamilton-Jacobi inequality (HJI) criterion. Further, in order to effectively filtrate external disturbances of the nonlinear stochastic coupling networks, synchronization robustness can be guaranteed by solving a HJI. That is, by solving these two HJI criteria, not only the asymptotical synchronizability in probability, but also the robust synchronizability is guaranteed. For simplifying the HJI criteria, linear matrix inequality (LMI) criteria are proposed based on the Takagi-Sugeno (T-S) fuzzy model. Finally, we propose an algorithm for the minimal coupling design to reduce the redundant Poisson diffusion couplings of the coupling networks without losing its asymptotical synchronizability in probability and synchronization robustness. A simulation example is provided to illustrate the minimal coupling design procedure and verify the robust synchronizability.

摘要...(i)
Abstract...(iii)
誌謝...(iv)
Contents...(v)
List of Figures...(vi)
I. Introduction...(1)
II. Preliminaries and Mathematical Models...(6)
III. Synchronization Error Dynamic and Analysis of Synchronizability...(12)
IV. Analysis of Synchronizability via T-S Fuzzy Approach...(17)
V. Robust Synchronization of the Nonlinear Stochastic Coupling Networks with External Disturbances...(21)
VI. Robust Synchronization Design with Minimal Coupling...(29)
VII. Simulation Example...(45)
VIII. Conclusion...(56)
Appendix...(57)
Reference...(65)

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