臺灣博碩士論文加值系統

在本論文中，我們針對單一通道傳輸的三階混沌同步系統，分別考慮在參數已知、參數未知、加入干擾量等不同的情況，以MRAC架構為基礎，設計適當的控制器來達成強健適應混沌同步的目的。
在文章中我們主要分成三個部分來討論。在第一部份，考慮傳送端參數已知的情況下，我們將證明存在一組最佳的控制器參數，使接收端與傳送端的系統達成同步；在第二部分，考慮參數未知的情況，我們加入適應性演算法估測控制器的參數，使系統會達到適應同步的目的；在第三部分，考慮外加干擾的情況，在這裡我們提出兩個控制法，分別是修正後的適應性演算法以及VS-MRAC演算法，用以確保系統不因外加的干擾量而不穩定，其中修正後的適應性控制法可以保證同步誤差在一定的範圍內，而VS-MRAC演算法更可以讓同步誤差仍然為零。
在論文中我們均有對所推得的理論做一數值上的模擬以驗證所推理論的可行性；最後將進一步以DSP實現我們所提出的混沌同步系統，探討這些方法在硬體實作上的應用性。

In this thesis, we develop a robust adaptive chaotic synchronization technique to achieve transmitting the information in one channel. There are three steps to setup a robust adaptive synchronization. Model reference control (MRC) and observable parametric model are first considered to model the control law and the chaotic systems under the system parameters are prior known.
Furthermore, a SPR-Lyapunov adaptive algorithm is derived to estimate the control parameters. Combing the SPR-Lyapunov adaptive algorithm and the observable parametric model, the scheme of MRAC are developed to achieve the adaptive synchronization under the system parameters are unknown. Finally, the robust adaptive strategy algorithm is proposed to treat the adaptive synchronization in the presence of noise. However, the results of systems simulation are shown that the robust adaptive synchronization is not efficient, because that the system error are not perfect. Therefore, VS-MRAC algorithm is proposed to overcome the problem. The advantage of VS-MRAC is that the synchronization error may decay to zero in the finite time. From the theorem and results of the VS-MRAC algorithm, the robust adaptive synchronization can be perfectly achieved.
In our thesis, we will do not only the numerical simulation to verify proposed theories but also an implementation to set up a proposed chaotic synchronization system based on DSP. From the results of DSP implementation, the VS-MRAC control method can not provide a perfect result as those of computer simulation. The main reason is that the sampling rate of AD/DA on DSP C6711 is 8k Hz. To improve the results, we will further modify the VSS algorithm and raise the sampling rate of AD/DA in future.

中文摘要 I
英文摘要 II
誌謝 IV
目錄 V
圖目錄 VI
第一章 緒論 1
1.1 文獻探討 1
1.2 研究動機及目的 5
1.3 研究方法及步驟 6
1.4 論文概述 7
第二章 具強健性之參考模型適應控制架構下的混沌同步設計 8
2.1 參考模型適應控制簡介 8
2.2 問題描述 9
2.3 MRC控制架構 10
2.3.1 MRC架構下的混沌同步系統設計 14
2.4 MRAC架構下的混沌同步系統設計 21
2.5 考慮有外加干擾時的混沌同步系統設計 31
2.6 結論 41
第三章 可變結構之參考模型適應控制架構下的混沌同步設計 42
3.1 可變結構控制簡介 42
3.2 問題描述 49
3.3 VS-MRAC架構下的混沌同步系統設計 50
3.4 結論 61
第四章 DSP硬體實現強健適應混沌同步傳輸系統 62
4.1 數位訊號處理器(DSP)簡介 62
4.1.1 數位訊號處理器(DSP)中央處理單元介紹 64
4.1.2 TI C6711 DSK模版之記憶體配置(Memory Maps) 68
4.1.3 開發軟體Code Composer Studio(CCS)介紹 70
4.2 問題描述及DSP硬體模擬結果 71
4.3 結論 80
第五章 總結與未來展望 81
5.1 總結 81
5.2未來展望 81
參考文獻 82
作者簡介 85

[1]E. N. Lorenz, “Deterministic nonperiodic flow,” J. of Atmos. Sci., Vol. 20, pp. 130-141, 1963.
[2]G. Lin and L. O. Chua, “Canonical Realization of Chua’s Circuit Family,” IEEE Trans. Circuit Sys., vol.37, pp.885-902, 1990.
[3]D. Romano, M. B. Vati and F. Meloni, ”Chua’s Atom,” Int. J. of Bifur. Chaos, vol.6, pp.1153-1157, 1999.
[4]G. Chen, “Controlling Chua’s Global Unfolding Circuit Family,” IEEE Trans. Circuits Sys., vol.40, pp.829-832, 1993.
[5]L. Pivka, C. W. Wu and A. Huang, ”Lorenz equation and Chua’s equation,” Int. J. of Bifur. Chaos, vol.6, pp.2443-2489, 1996.
[6]A. Volkovskii, ”Synchronization of chaotic systems using phase control,” IEEE Trans. Circuits Sys., vol.44, pp.913-917, 1997.
[7]S. Mascolo and G. Grassi, ”Controlling chaotic dynamics using backstepping design with application to the Lorenz system and Chua’s circuit,” Int. J. of Bifur. Chaos, vol.9, pp.1425-1434, 1999.
[8]Y. Z. Yin, ”Synchronization of chaos in a modified Chua’s circuit using continuous control,” Int. J. of Bifur. Chaos, vol.6, pp.2101-2117, 1996.
[9]H. Lenz and D. Obradovic, ”Robust control of the chaotic Lorenz system,” Int. J. of Bifur Chaos, vol.7, pp.2847-2854, 1997.
[10]G. Chen and X. Dong, ”On feedback control of chaotic continuous-time systems,” IEEE Trans. Circuits Sys., vol.40, pp.591-601, 1993.
[11]J. A. K. Suykens, P. F. Curran and L. O. Chua, ”Master-slave synchronization using dynamic output feedback,” Int. J. of Bifur. Chaos, vol.7, pp.671-679, 1997.
[12]T. Yang and L. O. Chua, ”Impulsivee stabilization for control and synchronization of chaotic systems: theory and application to secure communication,” IEEE Trans. Circuits Sys., vol.44, pp.976-988, 1997.
[13]T. L. Carroll and L. M. Pecora, “Synchronizing chaotic circuits,” IEEE Trans. Circuits Sys., vol. 38, pp. 453-456, 1991.
[14]O. Morgül and E. Solak, “Observer based synchronization of chaotic systems,” Physical Review E, vol. 54, pp. 4803-4809, 1996.
[15]H. Nijmeijer and I. M. Y. Mareels, “An observer looks at synchronization,” IEEE Trans. on Circuits and Systems-I, vol. 44, pp. 882-890, 1997.
[16]G. Grassi and S. Mascolo, “Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal,” IEEE Trans. on Circuits and Systems-I, vol. 44, pp. 1011-1014, 1997.
[17]M. Boutayeb, M. Darouach and H. Rafaralahy, “Generalized state-space observers for chaotic synchronization and secure communication,” IEEE Trans. on Circuits and Systems-I, vol. 49, pp. 345-349, 2002.
[18]M. Feki and B. Robert, “Observer-based chaotic synchronization in the presence of unknown inputs,” Chaos, Solitons and Fractals, vol. 15, pp. 831-840, 2003.
[19]K. M. Short, “Steps toward unmasking secure communications,” Int. J. of Bifurcation and Chaos, vol. 4, pp. 959-977, 1994.
[20]K. M. Short, “Unmasking a modulated chaotic communications scheme,” Int. J. of Bifurcation and Chaos, vol. 6, pp. 367-375, 1996.
[21]T. Yang, C. W. Wu and L. O. Chua, “Cryptography based on chaotic systems,” IEEE Trans. on Circuits and Systems-I, vol. 44, pp. 469-472, 1997.
[22]A. Rulkov, H. Nijmeijer, and A. Markov, “Adaptive observer-based synchronization for communication,” Int. J. Bifurcation Chaos, vol. 10, pp. 2807–2813, 2000.
[23]M. D. Bernardo, “An adaptive approach to the control and synchronization of continuous-time chaotic systems,” Int. J. Bifurcation Chaos, vol. 6, pp. 557–568, 1996.
[24]J. K. John and R. E. Amritkar, “Synchronization by feedback and adaptive control,” Int. J. Bifurcation Chaos, vol. 4, pp. 1687–1695, 1994.
[25]J.Wang and X.Wang, “Parametric adaptive control in nonlinear dynamical systems,” Int. J. Bifurcation Chaos, vol. 8, pp. 2215–2223, 1998.
[26]A. K. Kozlov, V. D. Shalfeev, and L. O. Chua, “Exact synchronization of mismatched chaotic systems,” Int. J. Bifurcation Chaos, vol. 6, pp. 569–580, 1996.
[27]C. W. Wu, Y. Tao, and L. O. Chua, “On adaptive synchronization and control of nonlinear dynamical systems,” Int. J. Bifurcation Chaos, vol. 6, pp. 455–471, 1996.
[28]A. L. Fradkov and A. Y. Markov, “Adaptive synchronization of chaotic systems based on speed gradient method and passification,” IEEE Trans .Circuits Syst. I, vol. 44, pp. 905–912, Oct. 1997.
[29]A. Y. Pogromsky, “Passivity based design of synchronizing systems,” Int. J. Bifurcation Chaos, vol. 8, pp. 295–319, 1998.
[30]Kuang-Yow Lian and Peter Liu, “Adaptive synchronization design for chaotic systems via a scalar driving signal,” IEEE Trans .Circuits Syst. I, vol. 49, pp. 17–27, Jan. 2002.
[31]Petros A. Ioannou and Jing Sun, “Robust adaptive control,” Prentice Hall PTR, 1996.
[32]陳永平，可變結構控制設計，全華科技股份有限公司，台北，1999。