Observers-based synchronization and input recovery for a class of nonlinear chaotic models

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 53, Issue 9, 2006, Pages 1977-1988

  Cherrier, Estelle ^a,b   Boutayeb, Mohamed ^c   Ragot, José ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

^b Faculté de Médecine   (France)

^c UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

Cryptosystem; Nonlinear observer; Synchronization; Time delayed chaotic system

Indexed keywords

ASYMPTOTIC STABILITY; CRYPTOGRAPHY; ESTIMATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; SYNCHRONIZATION;

LINEAR MATRIX INEQUALITIES; NONLINEAR OBSERVER; TIME-DELAYED CHAOTIC SYSTEM;

NONLINEAR SYSTEMS;

EID: 33749389947     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2006.882817     Document Type: Article

References (41)

1. L. Pecora and T. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett., vol. 64, no. 8, pp. 821-824, 1990.
2. T. Carroll and L. Pecora, "Synchronizing chaotic circuits," IEEE Trans. Circuit Syst., vol. 38, no. 4, pp. 453-456, Apr. 1991.
3. G. Kolumbán, M. P. Kennedy, and L. O. Chua, "The role of synchronization in digital communications using chaos - Part I: Fundamentals of digital communications," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 31, no. 9, pp. 927-936, Sep. 1997.
4. L. Kocarev, K. Halle, K. Eckert, L. Chua, and U. Parlitz, "Experimental demonstration of secure communications via chaotic synchronization," Int. J. Bifurc. Chaos, vol. 2, pp. 709-713, 1992.
5. K. Cuomo, A. Oppenheim, and S. Strogatz, "Synchronization of Lorenz-based chaotic circuits with applications to communications," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 40, no. 10, pp. 626-633, Oct. 1993.
6. G. Kolumbán, M. P. Kennedy, and L. O. Chua, "The role of synchronization in digital communications using chaos - Part II: Chaotic modulation and chaotic synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 31, pp. 1129-1140, 1998.
7. T. Yang, "A survey of chaotic secure communication systems," Int. J. of Comput. Cogn., vol. 2, no. 2, pp. 81-130, 2004.
8. K.-Y. Lian and P. Liu, "Synchronization with message embedded for generalized lorenz chaotic circuits and its error analysis," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 9, pp. 1418-1425, Sep. 2000.
9. C. Li, X. Liao, and K. Wong, "Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communications," Phys. D, vol. 194, pp. 187-202, 2004.
10. H. Dedieu, M. Kennedy, and M. Hasler, "Chaos shift keying: Modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 10, pp. 634-642, Oct. 1993.
11. K. Halle, C. Wu, M. Itoh, and L. Chua, "Spread spectrum communication through modulation of chaos," Int. J. Bifurc. Chaos, vol. 3, no. 2, pp. 469-477, 1993.
12. K. Short, "Steps towards unmasking secure communications," Int. J. Bifurc. Chaos, vol. 4, no. 4, pp. 959-977, 1994.
13. T. Yang, L.-B. Yang, and C.-M. Yang, "Breaking chaotic secure communication using a spectrogram," Phys. Lett. A, vol. 247, pp. 105-111, 1998.
14. T. Yang, C. Wu, and L. Chua, "Cryptography based on chaotic systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 5, pp. 469-472, May 1997.
15. Z.-P. Jiang, "A note on chaotic secure communication systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 92-96, Jan. 2002.
16. M. Sobhy and A.-E.-D. Shehata, "Secure computer communication using chaotic algorithms," Int. J. Bifurc. Chaos, vol. 10, no. 12, pp. 2831-2839, 2000.
17. T. Carroll and L. Pecora, "Cascading synchronized chaotic systems," Phys. D, vol. 67, pp. 126-140, 1993.
18. N. Corron and D. Hahs, "A new approach to communications using chaotic signals," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 5, pp. 373-382, May 1997.
19. S. Bu and B.-H. Wang, "Improving the security of chaotic encryption by using a simple modulating method," Chaos, Solitons, Fractals, vol. 19, pp. 919-924, 2004.
20. S. Tang, H. Chen, S. Hwang, and J. Liu, "Message encoding and decoding through chaos modulation in chaotic optical communications," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 2, pp. 163-169, Feb. 2002.
21. T.-L. Liao and N.-S. Huang, "An observer-based approach for chaotic synchronization with applications to secure communications," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 46, no. 9, pp. 1144-1150, Sep. 1999.
22. G. Millerioux and J. Daafouz, "Global chaos synchronization and robust filtering in noisy context," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 10, pp. 1170-1176, Oct. 2001.
23. M. Boutayeb, M. Darouach, and H. Rafaralahy, "Generalized state-space observers for chaotic synchronization and secure sommunication," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 3, pp. 345-349, Mar. 2002.
24. Q. Ha and H. Trinh, "State and input simultaneous estimation for a class of nonlinear systems," Automatica, vol. 40, pp. 1779-1785, 2004.
25. S. Čelikovský and G. Chen, "Secure synchronization of a class of chaotic systems from a nonlinear observer approach," IEEE Trans. Autom. Contr., vol. 50, no. 1, pp. 76-82, Jan. 2005.
26. G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking two secure communication systems based on chaotic masking," IEEE Trans. Circuits Syst. II, Expr. Briefs, vol. 51, no. 10, pp. 505-506, Oct. 2004.
27. G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking a secure communication scheme based on the phase synchronization of chaotic systems," Chaos, vol. 14, no. 2, pp. 274-278, 2004.
28. G. Alvarez and S. Li, Estimating short-time period to break different types of chaotic modulation based secure communications. (Jun. 2004) [Online]. Available: http://arxiv.org/abs/nlin.CD/0406039
29. G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Cryptanalyzing an improved security modulated chaotic encryption scheme using ciphertext absolute value," Chaos, Solitons, Fractals, vol. 23, no. 5, pp. 1749-1756, 2005.
30. G. Alvarez and S. Li, Cryptographic requirements for chaotic secure communications. (Nov. 2003) [Online]. Available: http://arxiv.org/abs/ nlin.CD/0311039
31. X. Wang, G. Chen, and X. Yu, "Anticontrol of chaos in continuous-time systems via time-delay feedback," Chaos, vol. 10, no. 4, pp. 771-779, 2000.
32. X. Wang, G.-Q. Zhong, K.-S. Tang, K. Man, and Z.-F. Liu, "Generating chaos in Chua's circuit via time-delay feedback," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 9, pp. 1151-1156, Sep. 2001.
33. E. Cherrier and M. Boutayeb, "Observer-based approach for synchronization of modified Chua's circuit," in Proc. NOLCOS, IFAC Symp. Nonlinear Control Systems, Stuttgart, Germany, 2004.
34. E. Cherrier, M. Boutayeb, and J. Ragot, "Observer-based approach for synchronization of a time-delayed Chua's circuit," in Proc. ISCAS, IEEE International Symp. Circuits Syst., Kobe, Japan, 2005.
35. M. Franz, "Chua's equation with cubic nonlinearity," Int. J. Bifurc. Chaos, vol. 6, pp. 2175-2222, 1996.
36. J. Farmer, "Chaotic attractors of an infinite-dimensional dynamical system," Phys. D, vol. 4, pp. 366-393, 1982.
37. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer-Verlag, 1990.
38. O. Morgül and E. Solak, "Observer based synchronization of chaotic systems," Physical Review E, vol. 54, no. 5, pp. 4803-4811, 1996.
39. H. Nijmeijer and I. Mareels, "An observer looks at synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 10, pp. 882-890, 1997.
40. G. Grassi and S. Mascolo, "Nonlinear observer design to synchronize systems via a scalar signal," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 10, pp. 640-656, Oct. 1997.
41. M. Feki, "Observer-based exact synchronization of ideal and mis-matched chaotic systems," Phys. Lett. A, vol. 309, pp. 53-60, 2003.