Home Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control
Article
Licensed
Unlicensed Requires Authentication

Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control

  • Yuangan Wang ORCID logo EMAIL logo and Dong Li
Published/Copyright: February 26, 2020

Abstract

Time delay is a common but not negligible phenomenon in nonlinear systems, which affects the performance of synchronization. Based on principles of intermittent control and Lyapunov stability theories, we establish the synchronization criteria of the time-delay chaotic systems via adaptive intermittent control. The proposed control scheme is under aperiodically intermittent control, which is also extended to periodically intermittent control to better realization. Finally, to verify the effectiveness of our results, we choose the Lorenz system to do simulation.

MSC 2010: 34K20; 34K37

Acknowledgements

This work is supported by the Qinzhou University Nurturing Fund for Projects of National Natural Science Foundation of China, Project No. 2014PY-GJ04 and the Foundation of Education Department of Guangxi, China, Project No.2013ZD072.

References

[1] S. Vaidyanathan, Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities, Eur. Phys. J-Spec. Top. 223(8) (2014), 1519–1529.10.1140/epjst/e2014-02114-2Search in Google Scholar

[2] D. Sadaoui, A. Boukabou and S. Hadef, Predictive feedback control and synchronization of hyperchaotic systems, Appl. Math. Comput. 247 (2014), 235–243.10.1016/j.amc.2014.09.016Search in Google Scholar

[3] X. Chen, J. H. Park, J. Cao and J. Qiu, Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances, Appl. Math. Comput. 308 (2017), 161–173.10.1016/j.amc.2017.03.032Search in Google Scholar

[4] A. Senouci and B. Abdelkrim, Predictive control and synchronization of chaotic and hyperchaotic systems based on a T–S fuzzy model, Math. Comput. Simulat. 105 (2014), 62–78.10.1016/j.matcom.2014.05.007Search in Google Scholar

[5] Y. Wang, H. Yu, X. Zhang and D. Li, Stability analysis and design of time-varying nonlinear systems based on impulsive fuzzy model, Discrete Dyn. Nat. Soc. 2 (2012), 373–390.10.1155/2012/192546Search in Google Scholar

[6] Y. Wang and H. Yu, Fuzzy synchronization of chaotic systems via intermittent control, Chaos Soliton Fract. 106 (2018), 154–160.10.1016/j.chaos.2017.11.024Search in Google Scholar

[7] X. F. Li, Y. D. Chu, A. Y. Leung and H. Zhang, Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls, Chaos Soliton Fract. 100 (2017), 24–30.10.1016/j.chaos.2017.04.033Search in Google Scholar

[8] X. Liu, Y. Liu and L. Zhou, Quasi-synchronization of nonlinear coupled chaotic systems via aperiodically intermittent pinning control, Neurocomputing. 173 (2016), 759–767.10.1016/j.neucom.2015.08.027Search in Google Scholar

[9] C. Hu and J. Yu, Generalized intermittent control and its adaptive strategy on stabilization and synchronization of chaotic systems, Chaos Soliton Fract. 91 (2016), 262–269.10.1016/j.chaos.2016.06.004Search in Google Scholar

[10] G. Wen, Q. G. Wang, C. Lin, G. Li and X. Han, Chaos synchronization via multivariable PID control, Int. J. Bifurcat. Chaos. 17(5) (2007), 1753–1758.10.1142/S0218127407018051Search in Google Scholar

[11] X. Liu, H. Su and M. Z. Chen, A switching approach to designing finite-time ]synchronization controllers of coupled neural networks, IEEE T. Neur. Net. Lear. 27(2) (2015), 471–482.10.1109/TNNLS.2015.2448549Search in Google Scholar PubMed

[12] X. Liu, D. W. Ho, Q. Song and W. Xu, Finite/fixed-time pinning synchronization of complex networks with stochastic disturbances, IEEE T. Cybernetics. 49(6) (2018), 2398–2403.10.1109/TCYB.2018.2821119Search in Google Scholar PubMed

[13] X. Liu, Q. G. Wang and C. Lin, Prespecified-time cluster synchronization of complex networks via a smooth control approach, IEEE T. Cybernetics. (2018). (Access paper, doi: 10.1109/TCYB.2018.2882519).Search in Google Scholar

[14] J. Cai and M. Ma, Synchronization between two non-autonomous chaotic systems via intermittent control of sinusoidal state error feedback, Optik. 130 (2017), 455–463.10.1016/j.ijleo.2016.10.075Search in Google Scholar

[15] Y. Dong and J. G. Xian, Finite-time Quasi-synchronization of two nonidentical chaotic systems via intermittent control, Commun. Theor. Phys. 66(3) (2016), 306–314.10.1088/0253-6102/66/3/306Search in Google Scholar

[16] T. Huang and C. Li, Chaotic synchronization by the intermittent feedback method, J. Comput. Appl. Math, 234(4) (2010), 1097–1104.10.1016/j.cam.2009.05.020Search in Google Scholar

[17] D. Li and X. Zhang, Impulsive synchronization of fractional order chaotic systems with time-delay, Neurocomputing. 216 (2016), 39–44.10.1016/j.neucom.2016.07.013Search in Google Scholar

[18] W. H. Chen, Z. Jiang, J. Zhong and X. Lu, On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays, J. Franklin. I. 351(8) (2014), 4084–4110.10.1016/j.jfranklin.2014.04.014Search in Google Scholar

[19] Y. Li and C. Li, Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period, Neurocomputing. 173 (2016), 1341–1347.10.1016/j.neucom.2015.09.007Search in Google Scholar

[20] Z. Wu, Exponential stabilization and synchronization of complex-variable chaotic systems via intermittent control, Int. J. Nonlinear Sci. Numer. Simul. 14(3–4) (2013), 189–194.10.1515/ijnsns-2012-0182Search in Google Scholar

[21] T. Huang, C. Li, W. Yu and G. Chen, Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback, Nonlinearity. 22(3) (2009), 569–584.10.1088/0951-7715/22/3/004Search in Google Scholar

[22] A. Abdurahman, M. Sader and H. Jiang, Improved results on adaptive control approach for projective synchronization of neural networks with time-varying delay, Int. J. Nonlinear Sci. Numer. Simul. 20(6) (2019), 623–631.10.1515/ijnsns-2018-0002Search in Google Scholar

[23] A. Muhammadhaji and A. Abdurahman, General decay synchronization for Fuzzy cellular neural networks with time-varying delays, Int. J. Nonlinear Sci. Numer. Simul. 20(5) (2019), 551–560.10.1515/ijnsns-2018-0041Search in Google Scholar

[24] R. Zhang, D. Zeng, J. H. Park, Y. Liu and S. Zhong, Quantized sampled-data control for synchronization of inertial neural networks with heterogeneous time-varying delays, IEEE T. Neur. Net. Lear. 29(12) (2018), 6385–6395.10.1109/TNNLS.2018.2836339Search in Google Scholar PubMed

[25] W. Zhang, C. Li, T. Huang and J. Huang, Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control, Neurocomputing. 173 (2016), 1066–1072.10.1016/j.neucom.2015.08.063Search in Google Scholar

[26] S. Cai, P. Zhou and Z. Liu, Intermittent pinning control for cluster synchronization of delayed heterogeneous dynamical networks, Nonlinear Anal-Hybri. 18 (2015), 134–155.10.1016/j.nahs.2015.06.007Search in Google Scholar

[27] M. Liu, H. Jiang and C. Hu, Synchronization of hybrid-coupled delayed dynamical networks via aperiodically intermittent pinning control, J. Franklin. I. 351(12) (2016), 2722–2742.10.1016/j.jfranklin.2016.05.012Search in Google Scholar

[28] R. Rifhat, A. Muhammadhaji and Z. Teng, Global Mittag–Leffler synchronization for impulsive fractional-order neural networks with delays, Int. J. Nonlinear Sci. Numer. Simul. 19(2) (2018), 205–213.10.1515/ijnsns-2017-0179Search in Google Scholar

Received: 2018-10-11
Accepted: 2020-02-02
Published Online: 2020-02-26
Published in Print: 2020-07-28

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 23.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ijnsns-2018-0308/html
Scroll to top button