×

Stabilization and synchronization of chaotic systems via intermittent control. (English) Zbl 1222.93194

Summary: We consider the stabilization and synchronization of chaotic systems via intermittent control with time varying control period and control width. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of nonlinear system. An effective adaptive-intermittent control law is also presented. Two examples are given to verify our proposed results.

MSC:

93D15 Stabilization of systems by feedback
34D06 Synchronization of solutions to ordinary differential equations
34H15 Stabilization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Halle, K.; Wu, C. W.; Itoh, M.; Chua, L. O., Spread spectrum communication through modulation of chaos, IEICE Trans Commun, 3, 469-477 (1993) · Zbl 0870.94002
[2] Madan, R., Chuas circuit: a paradigm for chaos (1993), World Scientific: World Scientific Singapore · Zbl 0861.58026
[3] Parlitz, U.; Chua, L. O.; Kocarev, L.; Halle, K. S.; Shang, A., Transmission of digital signals by chaotic synchronization, Int J Bifurcation Chaos, 2, 973-977 (1992) · Zbl 0870.94011
[4] Wu, C. W.; Chua, L. O., A simple way to synchronize chaotic systems with applications to secure communication systems, Int J Bifurcation Chaos, 3, 1619-1627 (1993) · Zbl 0884.94004
[5] Yang, T.; Wu, C. W.; Chua, L. O., Cryptography based on chaotic systems, IEEE Trans Circuits Syst, 44, 469-472 (1997) · Zbl 0884.94021
[6] Boccalettia, S.; Kurthsc, J.; Osipovd, G.; Valladaresb, D. L.; Zhou, C. S., The synchronization of chaotic systems, Phys Rep, 366, 1-101 (2002)
[7] Hu, G.; Pivka, L.; Zheleznyak, A. L., Synchronization of a one-dimensional array of Chuas circuits by feedback control and noise, IEEE Trans Circuits Syst, 42, 736-740 (1995)
[8] Jiang, G. P.; Chen, G. R.; Tang, W. K., A new criterion for chaos synchronization using linear state feedback control, Int J Bifurcation Chaos, 13, 2343-2351 (2003) · Zbl 1064.37515
[9] Lorĺ, A.; Zavala-Rĺo, A., Adaptive tracking control of chaotic systems with applications to synchronization, IEEE Trans Circuits Syst, 54, 2019-2029 (2007) · Zbl 1374.93184
[10] Huang, D. B., Simple adaptive-feedback controller for identical chaos synchronization, Phys Rev E, 71, 037203 (2005)
[11] Millerioux, G.; Daafouz, J., An observer-based approach for input-independent global chaos synchronization of discrete-time switched systems, IEEE Trans Circuits Syst, 50, 1270-1279 (2003) · Zbl 1368.93252
[12] Morgül, M.; Akgü, M., A switching synchronization scheme for a class of chaotic systems, Phys Lett A, 301, 241-249 (2002) · Zbl 0997.37013
[13] Yang, T.; Chua, L. O., Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication, IEEE Trans Circuits Syst, 44, 976-988 (1997)
[14] Yang, T., Impulsive control, IEEE Trans Autom Control, 44, 1081-1083 (1999) · Zbl 0954.49022
[15] Li, Z. G.; Wen, C. Y.; Soh, Y. C.; Xie, W. H., The stabilization and synchronization of Chuas oscillators via impulsive control, IEEE Trans Circuits Syst, 48, 1351-1355 (2001) · Zbl 1024.93052
[16] Stojanovski, T.; Kocarev, L.; Parlitz, U., Driving and synchronizing by chaotic impulses, Phys Rev E, 54, 2128-2131 (1996)
[17] Ömer, Morgül; Moez, Feki, Synchronization of chaotic systems by using occasional coupling, Phys Rev E, 55, 5004-5010 (1997)
[18] Huang, T. W.; Li, C. D.; Yu, W. W.; Chen, G. R., Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback, Nonlinearity, 22, 569-584 (2009) · Zbl 1167.34386
[19] Li, C. D.; Liao, X. F.; Huang, T. W., Exponential stabilization of chaotic systems with delay by periodically intermittent control, Chaos, 17, 013103 (2007) · Zbl 1159.93353
[20] Li, C. D.; Feng, G.; Liao, X. F., Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans Circuits Syst, 54, 1019-1023 (2007)
[21] Żochowski, M., Intermittent dynamical control, Physica D, 145, 181-190 (2000) · Zbl 0963.34030
[22] Amritkar, R. E.; Gupte, N., Synchronization of chaotic orbits: the effect of a finite time step, Phys Rev E, 47, 3889-3895 (1993)
[23] Huang, T. W.; Li, C. D.; Liu, X. Z., Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos, 18, 3, 033122 (2008) · Zbl 1309.34096
[24] Cheng, C. J.; Liao, T. L.; Yan, J. J.; Hwang, C. C., Exponential synchronization of a class of neural networks with time-varying delays, IEEE Trans Syst Man Cybern B, 36, 209-215 (2006)
[25] Liang, J.; Wang, Z. D.; Liu, Y.; Liu, X., Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances, IEEE Trans Syst Man Cybern B, 38, 1073-1083 (2008)
[26] Vincent, U. E.; Guo, R. W., A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems, Commun Nonlinear Sci Numer Simulat, 14, 3925-3932 (2009) · Zbl 1221.93134
[27] Mossa Al-Sawalha, M.; Noorani, M. S.M., Anti-synchronization of two hyperchaotic systems via nonlinear control, Commun Nonlinear Sci Numer Simulat, 14, 3402-3411 (2009) · Zbl 1221.37210
[28] Li, R. H., Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control, Commun Nonlinear Sci Numer Simulat, 14, 2757-2764 (2009) · Zbl 1221.93244
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.