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Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems. (English) Zbl 1250.34045
Summary: This paper is concerned with the design of the novel observer that synchronizes with the generalized Lorenz chaotic systems. A simple reduced-order observer scheme is proposed by including extra terms. The boundedness of the state variables in the original system is not necessary for the observer design. The prior knowledge on the derivative signal of the system output is not required. It is also shown that by adopting Lyapunov method and choosing appropriate design parameters, the synchronization (observation) errors can converge to zero exponentially. Finally, numerical examples are provided to illustrate the validity of the theoretical result.
34H10Chaos control (ODE)
34C28Complex behavior, chaotic systems (ODE)
[1]Pecora, L. M.; Caroll, T. L.: Synchronization in chaotic systems, Physical review letters 64, 821-824 (1990)
[2]Zhang, Z.; Shen, H.; Li, J.: Adaptive stabilization of uncertain unified chaotic systems with nonlinear input, Applied mathematics and computation 218, 4260-4267 (2011)
[3]Zhang, Z.; Wang, Y.; Du, Z.: Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters, Applied mathematics and computation 218, 6833-6840 (2012)
[4]Park, J. H.; Ji, D. H.; Won, S. C.; Lee, S. M.: H synchronization of time-delayed chaotic systems, Applied mathematics and computation 204, 170-177 (2008) · Zbl 1152.93027 · doi:10.1016/j.amc.2008.06.012
[5]Lee, S. M.; Kwon, O. M.; Park, J. H.: Synchronization of chaotic Lur’e systems with delayed feedback control using deadzone nonlinearity, Chinese physics B 21, 010506 (2011)
[6]Ji, D. H.; Park, J. H.; Lee, S. M.; Koo, J. H.; Won, S. C.: Synchronization criterion for Lur’e systems via delayed PD controller, Journal of optimization theory and applications 147, 298-317 (2010) · Zbl 1202.93138 · doi:10.1007/s10957-010-9723-0
[7]Ji, D. H.; Park, J. H.; Yoo, W. J.; Won, S. C.; Lee, S. M.: Synchronization criterion for Lur’e type complex dynamical networks with time-varying delay, Physics letters A 374, 1218-1227 (2010)
[8]Nijmeijer, H.; Mareels, I. M. Y.: An observer looks at synchronization, IEEE transactions on circuits and systems I 44, 882-890 (1997)
[9]Morgul, O.; Solak, E.: Observer based synchronization of chaotic systems, Physical review E 54, 4803-4811 (1996)
[10]Ushio, T.: Synthesis of synchronized chaotic systems based on observers, International journal of bifurcation and chaos 9, 541-546 (1999) · Zbl 0941.93533 · doi:10.1142/S0218127499000377
[11]Kailath, T.: Linear systems, (1980) · Zbl 0454.93001
[12]Zhang, Z.; Xu, S.; Shen, H.: Reduced-order observer-based output-feedback tracking control of nonlinear systems with state delay and disturbance, International journal of robust and nonlinear control 20, 1723-1738 (2010) · Zbl 1204.93062 · doi:10.1002/rnc.1544
[13]Solak, E.: A reduced-order observer for the synchronization of Lorenz systems, Physics letters A 325, 276-278 (2004) · Zbl 1161.37361 · doi:10.1016/j.physleta.2004.04.001
[14]Sun, Y. J.: A simple observer design of the generalized Lorenz chaotic systems, Physics letters A 374, 933-937 (2010)
[15]Sun, Y. J.: On the state reconstructor design for a class of chaotic systems, Chaos, solitons and fractals 40, 815-820 (2009) · Zbl 1197.37044 · doi:10.1016/j.chaos.2007.08.028
[16]Sun, Y. J.: An exponential observer for the generalized Rössler chaotic system, Chaos, solitons and fractals 40, 2457-2461 (2009) · Zbl 1198.93204 · doi:10.1016/j.chaos.2007.10.038
[17]Boutayeb, M.; Darouach, M.; Rafaralahy, H.: Generalized state-space observers for chaotic synchronization and secure communication, IEEE transactions on circuits and systems I 49, 345-349 (2002)
[18]Lorı&acute, A.; A; Panteley, E.; Zavala-Rı&acute, A.; O: Adaptive observers with persistency of excitation for synchronization of chaotic systems, IEEE transactions on circuits and systems I 56, 2703-2716 (2009)
[19]Sun, Y. J.: Solution bounds of generalized Lorenz chaotic systems, Chaos, solitons and fractals 40, 691-696 (2009) · Zbl 1197.37043 · doi:10.1016/j.chaos.2007.08.015
[20]Lü, J.; Chen, G.; Cheng, D.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, International journal of bifurcation and chaos 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[21]Lorenz, E. N.: Deterministic non-periods flows, Journal of the atmospheric sciences 20, 130-141 (1963)
[22]Chen, G.; Ueta, T.: Yet another chaotic attractor, International journal of bifurcation and chaos 9, 1465-1466 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[23]Lü, J.; Chen, G.: A new chaotic attractor coined, International journal of bifurcation and chaos 12, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620