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Abstract: We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.

基于滑模和反馈控制的鲁棒混沌系统同步

[1]Besancon, G., 2000. Remarks on nonlinear adaptive observer design. Syst. Contr. Lett., 41(4):271-280.

[2]Bowong, S., 2004. Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. Phys. Lett. A, 326(1-2):102-113.

[3]Chen, M., Kurths, J., 2007. Chaos synchronization and parameter estimation from a scalar output signal. Phys. Rev. E, 76(2):027203.

[4]Collins, J.J., Stewart, I.N., 1993. Coupled nonlinear oscillators and the symmetries of animal gaits. J. Nonl. Sci., 3(1):349-392.

[5]Feki, M., 2003. An adaptive chaos synchronization scheme applied to secure communication. Chaos Sol. Fract., 18(1):141-148.

[6]Femat, R., Solis-Perales, G., 2008. Robust Synchronization of Chaotic Systems via Feedback. Springer.

[7]Femat, R., Alvarez-Ramirez, J., Castillo-Toledo, B., et al., 1999. On robust chaos suppression in a class of nonlinear oscillators: application to Chua's circuit. IEEE Trans. Circ. Syst. I, 46(9):1150-1152.

[8]Femat, R., Alvarez-Ramirez, J., Fernandez-Anaya, G., 2000. Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization. Phys. D, 139(3-4):231-246.

[9]Femat, R., Ortiz, R.J., Perales, G.S., 2001. An adaptive chaos synchronization scheme applied to secure communication scheme via robust asymptotic feedback. IEEE Trans. Circ. Syst. I, 48(10):1161-1169.

[10]Freitas, U.S., Macau, E.E.N., Grebogi, C., 2005. Using geometric control and chaotic synchronization to estimate an unknown model parameter. Phys. Rev. E, 71(4):047203.

[11]Grassi, G., Mascoio, S., 1999. Synchronizing hyperchaotic systems by observer design. IEEE Trans. Circ. Syst. II, 46(4):478-483.

[12]Haefner, J.W., 2005. Modeling Biological Systems: Principles and Applications. Springer, New York, USA.

[13]Han, J.Q., 1995. The extended state observer of a class of uncertain systems. Contr. & Dec., 110(1):85-88 (in Chinese).

[14]Isidori, A, 1989. Nonlinear Control System. Springer-Verlag, Berlin, Germany.

[15]Karimi, H.R., 2011. Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations. Int. J. Contr. Automat. Syst., 9(4):671-680.

[16]Karimi, H.R., 2012. A sliding mode approach to H_∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. J. Franklin Inst., 349(4):1480-1496.

[17]Karimi, H.R., Gao, H., 2010. New delay-dependent exponential H_∞ synchronization for uncertain neural networks with mixed time-delays. IEEE Trans. Syst. Man Cybern. Part B, 40(1):173-185.

[18]Kocarev, L., Parlitz, U., 1995. General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett., 74(25):5028-5031.

[19]Levant, A., 2003. Higher-order sliding modes, differentiation and output-feedback control. Int. J. Contr., 76(9-10):924-941.

[20]Levant, A., Pavlov, Y., 2008. Generalized homogeneous quasi-continuous controllers. Int. J. Robust Nonl. Contr., 18(4-5):385-398.

[21]Li, X.R., Zhao, L.Y., Zhao, G.Z., 2005. Sliding mode control for synchronization of chaotic systems with structure or parameter mismatching. J. Zhejiang Univ.-Sci., 6(6):571-576.

[22]Liu, Y., Tang, W., 2009. Adaptive synchronization of chaotic systems and its uses in cryptanalysis. In: Recent Advances in Nonlinear Dynamics and Synchronization (NDS-1), Theory and Applications. Springer, 254:307-346.

[23]Liu, Y., Tang, W., Kocarev, L., 2008. An adaptive observer design for the auto-synchronization of Lorenz system. Int. J. Bifurcat. Chaos, 18(8):2415-2423.

[24]Mao, Y., 2009. Adaptive Synchronization and Its Use in Biological Neural Network Modeling. MS Thesis, City University of Hong Kong, Hong Kong, China.

[25]Mao, Y., Tang, W., Liu, Y., et al., 2009. Identification of biological neurons using adaptive observers. Cogn. Process., 10(Suppl 1):41-53.

[26]Nijmeijer, H., Mareels, I.M.Y., 1997. An observer looks at synchronization. IEEE Trans. Circ. Syst. I, 44(10):882-890.

[27]Pecora, L.M., Carroll, T.L., 1990. Synchronization in chaotic systems. Phys. Rev. Lett., 64(8):821-824.

[28]Pecora, L.M., Carroll, T.L., 1991. Driving systems with chaotic signals. Phys. Rev. A, 44(4):2374-2383.

[29]Rodriguez, A., de Leon, J., Fridman, L., 2008. Quasi-continuous high-order sliding-mode controllers for reduced-order chaos synchronization. Int. J. Nonl. Mech., 43(9):948-961.

[30]Trentelman, H.L., Takaba, K., Monshizadeh, N., 2013. Robust synchronization of uncertain linear multi-agent systems. IEEE Trans. Automat. Contr., 58(6):1511-1523.

[31]Wang, B., Shi, P., Karimi, H.R., et al., 2012. H_∞ robust controller design for the synchronization of master-slave chaotic systems with disturbance input. Model. Identif. Contr., 33(1):27-34.

[32]Wang, Y., Chik, D.T.M., Wang, Z.D., 2000. Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons. Phys. Rev. E, 61(1):740-746.

[33]Wittmeier, S., Song, G., Duffin, J., et al., 2008. Pacemakers handshake synchronization mechanism of mammalian respiratory rhythmogenesis. PNAS, 105(46):18000-18005.

[34]Xu, J., Min, L., Chen, G., 2004. A chaotic communication scheme based on generalized synchronization and hash functions. Chin. Phys. Lett., 21(8):1445-1448.

[35]Yang, T., Shao, H.H., 2002. Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design. Phys. Rev. E, 65(4):046210.

[36]Youssef, T., Chadli, M., Karimi, H.R., et al., 2013. Chaos synchronization based on unknown input proportional multiple-integral fuzzy observer. Abstr. Appl. Anal., 2013:670878.

[37]Yu, D., Parlitz, U., 2008. Estimating parameters by autosynchronization with dynamics restrictions. Phys. Rev. E, 77(6 Pt 2):066221.