Abstract
Here, observer based synchronization and secure communication scheme is presented for chaotic systems. In proposed scheme, extended Kalman filter based receiver is selected for given transmitter system. The stability results are derived using virtual system concept. Observer gains for synchronization are obtained as a solution of matrix Riccati equation. For secure communication, n-shift ciphering algorithm is used with one of the chaotic state chosen as key. Numerical simulations are presented in the end to verify the efficacy of proposed scheme.
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Pecora, L.M., Carroll, T.L.: Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 821–824 (1990)
Carroll, T.L., Pecora, L.M.: Synchronizing Chaotic Circuits. IEEE Trans. Circ. Syst.-I 38(4), 453–456 (1991)
Yang, L.X., Chu, Y.D., Zhang, J.G., Li, F.L., Chang, Y.X.: Chaos Synchronization in Autonomous Chaotic System via Hybrid Feedback Control. Chaos, Solitons and Fractals 41(1), 214–223 (2009)
Yang, T., Wu, C.W., Chua, L.O.: Cryptography based on Chaotic Systems. IEEE Trans. on Circ. Syst.-I 44(5), 469–472 (1997)
Boutayeb, M., Darouach, M., Rafaralahy, H.: Generalized State-space Observers for Chaotic Synchronization with Applications to Secure Communication. IEEE Trans. Circ. Syst.-I 49(3), 345–349 (2002)
Fallahi, K., Raoufi, R., Khoshbin, H.: An Application of Chen System for Secure Chaotic Communication based on Extended Kalman Filter and Multi-Shift Cipher Algorithm. Comm. in Nonlinear Science and Num. Sim. 13(4), 763–781 (2008)
Grassi, G., Mascolo, S.: Nonlinear Observer Design to Synchronize Hyperchaotic Systems via a Scalar Signal. IEEE Trans. Circ. Syst.-I 44(10), 1011–1014 (1997)
Liao, T.L., Huang, N.S.: An Observer based Approach for Chaotic Synchronization and Secure Communication. IEEE Trans. Circ. Syst.-I 46(9), 1144–1149 (1999)
Morgul, O., Solak, E.: Observer based Synchronization of Chaotic Systems. Phys. Rev. E 54(5), 4803–4811 (1996)
Lohmiller, W.: Contraction Analysis of Nonlinear Systems, Ph.D. Thesis, Department of Mechanical Engineering, MIT (1999)
Lohmiller, W., Slotine, J.J.E.: On Contraction Analysis for Nonlinear Systems. Automatica 34(6), 683–696 (1998)
Jouffroy, J., Slotine, J.J.E.: Methodological Remarks on Contraction Theory. In: IEEE Conf. on Decision Control, Atlantis, Bahamas, pp. 2537–2543 (2004)
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Sharma, B.B., Kar, I.N. (2009). Chaotic Synchronization and Secure Communication Using Contraction Theory. In: Chaudhury, S., Mitra, S., Murthy, C.A., Sastry, P.S., Pal, S.K. (eds) Pattern Recognition and Machine Intelligence. PReMI 2009. Lecture Notes in Computer Science, vol 5909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11164-8_89
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DOI: https://doi.org/10.1007/978-3-642-11164-8_89
Publisher Name: Springer, Berlin, Heidelberg
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