廣義羅倫斯混沌系統之保證指數同步的線性回授控制器設計及其應用

Exponential Synchronization and Application of Generalized Lorenz Chaotic Systems via Linear Feedback Control

呂政翰(Cheng-Han LU)

指導教授 ： 孫永莒

義守大學/電機資訊學院/電機工程學系/碩士(2015年)

https://doi.org/10.6343/ISU.2015.00166

摘要

在本篇論文中，本論文提出指數同步化的概念，同時針對廣義型Lorenz系統的同步化問題做探討。利用李雅普諾夫的方法論，針對廣義型的Lorenz系統，本論文提出一套簡易的線性控制器，促使整個系統達成指數同步化的標的。在此同時，上述系統的指數收斂速率將可被事先安排。最終，本論文將提出一套混沌保密通訊系統之實際應用，並輔以多個數值模擬結果來說明本論文主要定理的正確性及實用性。

關鍵字

混沌系統 ； 指數同步化 ； 線性控制器 ； 廣義型的Lorenz混沌系統

並列摘要

In this thesis, the concept of exponential synchronization is introduced and the chaos synchronizationof generalized Lorenz chaotic systemsis investigated. Based on the Lyapunov approach, a simple linear control is proposed to realize exponential synchronization for the generalized Lorenz chaotic systems. Moreover, the guaranteed exponential convergence rate can be pre-specified. Finally, some numerical simulations with application are provided to demonstrate the feasibility and effectiveness of the obtained result.
Keywords: Chaotic system; Exponential Synchronization; Linear control; Generalized Lorenz chaotic systems.

並列關鍵字

Chaotic system ； Exponential Synchronization ； Linear control ； Generalized Lorenz chaotic systems

參考文獻

[18] C.F. Chuang, W.J. Wang, Y.J. Sun, Y.J. Chen, T-S fuzzy model based H∞ finite-time synchronization design for chaotic systems. International Journal of Fuzzy Systems, 13 (4), pp. 358-368, 2011.

[19] Y.J. Sun, Composite tracking control for generalized practical synchronization of Duffing-Holmes systems with parameter mismatching, unknown external excitation, plant uncertainties, and uncertain deadzone nonlinearities. Abstract and Applied Analysis, 2012, Article ID 640568, 11 pages, doi:10.1155/2012/640568, 2012.

[20] Y.J. Sun, Nonlinear observer design of the generalized Rösslerhyperchaotic systems via DIL methodology, Mathematical Problems in Engineering, 2012, Article ID 764798, 9 pages, doi:10.1155/2012/764798, 2012.

[23] Y.J. Sun, DII-based linear feedback control design for practical synchronization of chaotic systems with uncertain input nonlinearity and application to secure communication. Abstract and Applied Analysis, 2012, Article ID 369267, 14 pages, doi:10.1155/2012/369267, 2012.

[1] Y.J. Sun,Solution bounds of generalized Lorenz chaotic systems. Chaos, Solitons & Fractals, 40 (2), pp. 691-696, 2009.