Pinning-controlled synchronization of partially coupled dynamical networks via impulsive control

Jin Cheng; Jin Cheng

doi:10.3934/math.2022008

AIMS Mathematics

2022, Volume 7, Issue 1: 143-155. doi: 10.3934/math.2022008

Previous Article Next Article

Research article

Pinning-controlled synchronization of partially coupled dynamical networks via impulsive control

Jin Cheng ^,

School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, China

Received: 15 August 2021 Accepted: 30 September 2021 Published: 08 October 2021
MSC : 34K20, 34K45, 35R12

In this paper, global exponential outer synchronization of coupled nonlinear systems with general coupling matrices are investigated via pinning impulsive control. More realistic and more general partially coupled drive-response systems are established, where the completely communication channel matrix between coupled nodes may not be a permutation matrix. By using pinning impulsive strategy involving pinning ratio and our generalised lower average impulsive interval method, a number of novel and less restrictive synchronization criteria are proposed. In the end, a numerical example is constructed to indicate the effectiveness of our theoretical results.
- complex dynamical networks,
- discontinuous control,
- pinning synchronization,
- impulsive control,
- outer synchronization
Citation: Jin Cheng. Pinning-controlled synchronization of partially coupled dynamical networks via impulsive control[J]. AIMS Mathematics, 2022, 7(1): 143-155. doi: 10.3934/math.2022008

Related Papers:

Abstract

In this paper, global exponential outer synchronization of coupled nonlinear systems with general coupling matrices are investigated via pinning impulsive control. More realistic and more general partially coupled drive-response systems are established, where the completely communication channel matrix between coupled nodes may not be a permutation matrix. By using pinning impulsive strategy involving pinning ratio and our generalised lower average impulsive interval method, a number of novel and less restrictive synchronization criteria are proposed. In the end, a numerical example is constructed to indicate the effectiveness of our theoretical results.

References

[1]	P. Erdös, A. Rényi, On the evolution of random graphs, Mathematical Institute of the Hungarian Academy of Sciences, 5 (1960), 17–61.
[2]	X. D. Li, D. Regan, H. Akca, Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays, IMA J. Appl. Math., 80 (2015), 85–99. doi: 10.1093/imamat/hxt027. doi: 10.1093/imamat/hxt027
[3]	A. Pratap, R. Raja, J. Alzabut, J. D. Cao, G. Rajchakit, C. X. Huang, Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field, Math. Method. Appl. Sci., 43 (2020), 6223–6253. doi: 10.1002/mma.6367. doi: 10.1002/mma.6367
[4]	T. T. Wang, L. Xu, J. B. Li, SDCRKL-GP: Scalable deep convolutional random kernel learning in gaussian process for image recognition, Neurocomputing, 456 (2021), 288–298. doi: 10.1016/j.neucom.2021.05.092. doi: 10.1016/j.neucom.2021.05.092
[5]	W. M. Wu, F. K. Zhang, C. Wang, C. Z. Yuan, Dynamical pattern recognition for sampling sequences based on deterministic learning and structural stability, Neurocomputing, 458 (2021), 376–389. doi: 10.1016/j.neucom.2021.06.001. doi: 10.1016/j.neucom.2021.06.001
[6]	F. Wang, Y. R. Sun, Self-organizing peer-to-peer social networks, Comput. Intell., 24 (2008), 213–233. doi: 10.1111/j.1467-8640.2008.00328.x. doi: 10.1111/j.1467-8640.2008.00328.x
[7]	B. Huberman, L. Adamic, Growth dynamics of the world-wide-web, Nature, 401 (1999), 131.
[8]	G. Rajchakit, Robust stability and stabilization of nonlinear uncertain stochastic switched discrete-time systems with interval time-varying delays, Appl. Math. Inf. Sci., 6 (2012), 555–565.
[9]	X. D. Li, J. H. Shen, H. Akca, R. Rakkiyappan, LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter, Appl. Math. Comput., 250 (2015), 798–804. doi: 10.1016/j.amc.2014.10.113. doi: 10.1016/j.amc.2014.10.113
[10]	C. Maharajan, R. Raja, J. D. Cao, G. Rajchakitd, Z. W. Tu, A. Alsaedi, LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach, Appl. Math. Comput., 326 (2018), 33–55. doi: 10.1016/j.amc.2018.01.001. doi: 10.1016/j.amc.2018.01.001
[11]	X. S. Yang, Z. C. Yang, X. B. Nie, Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 1529–1543. doi: 10.1016/j.cnsns.2013.09.012. doi: 10.1016/j.cnsns.2013.09.012
[12]	G. Ling, X. Z. Liu, M. F. Ge, Y. H. Wu, Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control, J. Franklin Inst., 358 (2021), 3193–3214. doi: 10.1016/j.jfranklin.2021.02.004. doi: 10.1016/j.jfranklin.2021.02.004
[13]	W. L. He, T. H. Luo, Y. Tang, W. L. Du, Y. C. Tian, F. Qian, Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy, IEEE T. Neur. Net. Lear., 31 (2020), 3334–3345. doi: 10.1109/TNNLS.2019.2943548. doi: 10.1109/TNNLS.2019.2943548
[14]	J. Q. Lu, D. W. C. Ho, Globally exponential synchronization and synchronizability for general dynamical networks, IEEE T. Syst. Man Cy.-S, 40 (2010), 350–361. doi: 10.1109/TSMCB.2009.2023509. doi: 10.1109/TSMCB.2009.2023509
[15]	N. Wang, X. C. Li, J. Q. Lu, F. E. Alsaadi, Unified synchronization criteria in an array of coupled neural networks with hybrid impulses, Neural Networks, 101 (2018), 25–32. doi: 10.1016/j.neunet.2018.01.017. doi: 10.1016/j.neunet.2018.01.017
[16]	X. S. Yang, Q. Song, J. D. Cao, J. Q. Lu, Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control, IEEE T. Neur. Net. Lear., 30 (2019), 951–958. doi: 10.1109/TNNLS.2018.2853650. doi: 10.1109/TNNLS.2018.2853650
[17]	X. S. Yang, Y. Liu, J. D. Cao, L. Rutkowski, Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching, IEEE T. Neur. Net. Lear., 31 (2020), 5483–5496. doi: 10.1109/TNNLS.2020.2968342. doi: 10.1109/TNNLS.2020.2968342
[18]	J. Liu, H. Q. Wu, J. D. Cao, Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity, Commun. Nonlinear Sci., 90 (2020), 105400. doi: 10.1016/j.cnsns.2020.105400. doi: 10.1016/j.cnsns.2020.105400
[19]	X. H. Wang, H. Q. Wu, J. D. Cao, Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth, Nonlinear Anal.-Hybrid., 37 (2020), 100888. doi: 10.1016/j.nahs.2020.100888. doi: 10.1016/j.nahs.2020.100888
[20]	J. T. Shen, P. Wang, X. J. Wang, A controlled strengthened dominance relation for evolutionary many-objective optimization, IEEE T. Cybernetics, 136 (2020), 3015998. doi: 10.1109/TCYB.2020.3015998. doi: 10.1109/TCYB.2020.3015998
[21]	C. P. Li, W. G. Sun, J. Kurths, Synchronization between two coupled complex networks, Phys. Rev. E, 76 (2007), 046204. doi: 10.1103/PhysRevE.76.046204. doi: 10.1103/PhysRevE.76.046204
[22]	H. W. Tang, L. Chen, J. A. Lu, C. K. Tse, Adaptive synchronization between two complex networks with nonidentical topological structures, Physica A., 387 (2008), 5623–5630. doi: 10.1016/j.physa.2008.05.047. doi: 10.1016/j.physa.2008.05.047
[23]	X. Q. Wu, W. X. Zheng, J. Zhou, Generalized outer synchronization between complex dynamical networks, Chaos, 19 (2009), 013109. doi: 10.1063/1.3072787. doi: 10.1063/1.3072787
[24]	J. B. Zhang, A. C. Zhang, J. D. Cao, J. L. Qiu, F. E. Alsaadi, Adaptive outer synchronization between two delayed oscillator networks with cross couplings, Sci. China Inf. Sci., 63 (2020), 209204. doi: 10.1007/s11432-018-9843-x. doi: 10.1007/s11432-018-9843-x
[25]	X. D. Li, X. Y. Yang, T. W. Huang, Persistence of delayed cooperative models: Impulsive control method, Appl. Math. Comput., 342 (2019), 130–146. doi: 10.1016/j.amc.2018.09.003. doi: 10.1016/j.amc.2018.09.003
[26]	H. L. Yang, X. Wang, S. M. Zhong, L. Shu, Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control, Appl. Math. Comput., 320 (2018), 75–85. doi: 10.1016/j.amc.2017.09.019. doi: 10.1016/j.amc.2017.09.019
[27]	X. Wang, J. H. Park, H. L. Yang, S. M. Zhong, A new settling-time estimation protocol to finite-time synchronization of impulsive memristor-based neural networks, IEEE T. Cybernetics, 2020, 3025932. doi: 10.1109/TCYB.2020.3025932.
[28]	D. Yang, X. D. Li, J. H. Shen, Z. J. Zhou, State-dependent switching control of delayed switched systems with stable and unstable modes, Math. Method. Appl. Sci., 41 (2018), 6968–6983. doi: 10.1002/mma.5209. doi: 10.1002/mma.5209
[29]	D. S. Xu, Y. Liu, M. Liu, Finite-time synchronization of multi-coupling stochastic fuzzy neural networks with mixed delays via feedback control, Fuzzy Set Syst., 411 (2021), 85–104. doi: 10.1016/j.fss.2020.07.015. doi: 10.1016/j.fss.2020.07.015
[30]	H. H. Ji, B. T. Cui, X. Z. Liu, Networked sampled-data control of distributed parameter systems via distributed sensor networks, Commun. Nonlinear Sci., 98 (2021), 105773. doi: 10.1016/j.cnsns.2021.105773. doi: 10.1016/j.cnsns.2021.105773
[31]	X. G. Tan, J. D. Cao, Intermittent control with double event-driven for leader-following synchronization in complex networks, Appl. Math. Model., 64 (2018), 372–385. doi: 10.1016/j.apm.2018.07.040. doi: 10.1016/j.apm.2018.07.040
[32]	Y. Xu, S. Gao, W. X. Li, Exponential stability of fractional-order complex multi-links networks with aperiodically intermittent control, IEEE T. Neural Networ., 32 (2021), 4063–4074. doi: 10.1109/TNNLS.2020.3016672. doi: 10.1109/TNNLS.2020.3016672
[33]	F. Liu, Q. Song, G. H. Wen, J. D. Cao, X. S. Yang, Bipartite synchronization in coupled delayed neural networks under pinning control, Neural Networks, 108 (2018), 146–154. doi: 10.1016/j.neunet.2018.08.009. doi: 10.1016/j.neunet.2018.08.009
[34]	X. Wang, X. Z. Liu, K. She, S. M. Zhong, Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes, Nonlinear Anal.-Hybrid, 26 (2017), 307–318. doi: 10.1016/j.nahs.2017.06.005. doi: 10.1016/j.nahs.2017.06.005
[35]	V. I. Utkin, H. C. Chang, Sliding mode control on electro-mechanical systems, Math. Probl. Eng., 8 (2002), 635132. doi: 10.1080/10241230306724. doi: 10.1080/10241230306724
[36]	X. G. Tan, J. D. Cao, X. D. Li, Consensus of leader-following multiagent systems: A distributed event-triggered impulsive control strategy, IEEE T. Cybernetics, 49 (2019), 792–801. doi: 10.1109/TCYB.2017.2786474. doi: 10.1109/TCYB.2017.2786474
[37]	Y. Yang, J. W. Xia, J. L. Zhao, X. D. Li, Z. Wang, Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays, Nonlinear Anal. Model. Control, 24 (2019), 696–717.
[38]	D. X. Peng, X. D. Li, R. Rakkiyappan, Y. H. Ding, Stabilization of stochastic delayed systems: Event-triggered impulsive control, Appl. Math. Comput., 401 (2021), 126054. doi: 10.1016/j.amc.2021.126054. doi: 10.1016/j.amc.2021.126054
[39]	X. D. Li, D. O. Regan, H. Akca, Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays, IMA J. Appl. Math., 80 (2015), 85–99. doi: 10.1093/imamat/hxt027. doi: 10.1093/imamat/hxt027
[40]	Y. S. Zhao, X. D. Li, J. D. Cao, Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency, Appl. Math. Comput., 386 (2020), 125467. doi: 10.1016/j.amc.2020.125467. doi: 10.1016/j.amc.2020.125467
[41]	W. H. Chen, Z. Y. Jiang, X. M. Lu, S. X. Luo, $H^{\infty}$ Synchronization for complex dynamical networks with coupling delays using distributed impulsive control, Nonlinear Anal.-Hybrid, 17 (2015), 111–127. doi: 10.1016/j.nahs.2015.02.004. doi: 10.1016/j.nahs.2015.02.004
[42]	H. L. Li, J. D. Cao, C. Hu, L. Zhang, Z. L. Wang, Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control, Neurocomputing, 356 (2019), 31–39. doi: 10.1016/j.neucom.2019.04.059. doi: 10.1016/j.neucom.2019.04.059
[43]	X. F. Wang, G. R. Chen, Pinning control of scale-free dynamical networks, Physica A, 310 (2002), 521–531.
[44]	W. W. Yu, G. R. Chen, J. H. Lu, On pinning synchronization of complex dynamical networks, Automatica, 45 (2009), 429–435. doi: 10.1016/j.automatica.2008.07.016. doi: 10.1016/j.automatica.2008.07.016
[45]	J. Q. Lu, C. D. Ding, J. G. Lou, J. D. Cao, Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers, J. Franklin I., 352 (2015), 5024–5041. doi: 10.1016/j.jfranklin.2015.08.016. doi: 10.1016/j.jfranklin.2015.08.016
[46]	X. C. Li, N. Wang, J. Q. Lu, F. E. Alsaadi, Pinning outer synchronization of partially coupled dynamical networks with complex inner coupling matrices, Physics A, 515 (2019), 497–509. doi: 10.1016/j.physa.2018.09.095. doi: 10.1016/j.physa.2018.09.095
[47]	W. L. He, F. Qian, J. D. Cao, Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Networks, 85 (2017), 1–9. doi: 10.1016/j.neunet.2016.09.002. doi: 10.1016/j.neunet.2016.09.002

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)