Abstract
This paper considers the finite-time synchronization problem of stochastic complex networks with mixed delays. A controller based on adaptive aperiodic intermittent control strategy is constructed, which can guarantee that network systems with unknown characteristics of the controlled object or a wide range of disturbance characteristics achieve synchronization in the finite-time. Moreover, relying on various inequality techniques, the finite-time synchronization criterion is obtained by establishing the Lyapunov function. Then, the synchronization of the stochastic network system can still be achieved, when the stochastic disturbance does not exist. Finally, the rationality of the theoretical results is tested by an example of Chua’s circuit system.
Similar content being viewed by others
References
E. J. Mark and Newman, “The structure and function of complex networks,” SIAM Review, pp. 167–256, 2013.
H. H. Wu, J. Wen, P. Han, H. J. Xing, X. Q. Zhang, C. S. Jia, and J. Shi, “The explorationon on the the characteristics of acupoint selection and the rule of acupoint combination in treatment of insomnia with acupuncture and moxibustion,” Complex Network Analysis, vol. 32, pp. 61–69, 2022.
X. X. Liu, Z. H. Yang, Z. W. Zhou, Y. Y. Sun, H. F. Lin, J. Wang, and B. Xu, “The impact of protein interaction networks’ characteristics on computational complex detection methods,” Journal of Theoretical Biology, vol. 439, no. 14, pp. 145–151, 2021.
P. Alapuranen and J. Schroeder, “Complex artificial neural network with applications to wireless communications,” Digital Signal Processing, vol. 119, 103194, 2021.
H. Shen, Z. G. Huang, Z. G. Wu, J. D. Cao, and J. H. Park, “Nonfragile H ∞ synchronization of BAM inertial neural networks subject to persistent dwell-time switching regularity,” IEEE Transactions on Cybernetics, vol. 52, no. 7, pp. 6591–6602, 2022.
H. Shen, X. H. Hu, J. Wang, J. D. Cao, and W. H. Qian, “Non-fragile H ∞ synchronization for Markov jump singularly perturbed coupled neural networks subject to double-layer switching regulation,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–11, 2021. DOI: https://doi.org/10.1109/TNNLS.2021.3107607
X. Ling, W. B. Ju, N. Guo, C. Y. Wu, and X. M. Xua, “Explosive synchronization in network of mobile oscillators,” Physics Letters A, vol. 384, no. 35, p. 12688117, 2020.
I. A. Shepelev, S. S. Muni, and T. E. Vadivasova, “Synchronization of wave structures in a heterogeneous multiplex network of 2D lattices with attractive and repulsive intra-layer coupling,” Chaos, vol. 31, no. 2, 021104, 2021.
N. Liu, J. Fang, W. Deng, Z. J. Wu, and G. Q. Ding, “Synchronization for a class of fractional-order linear complex networks via impulsive control,” International Journal of Control, Automation, and Systems, vol. 16, pp. 2839–2844, 2018.
X. W. Liu and T. P. Chen, “Finite-time and fixed-time cluster synchronization with or without pinning control,” IEEE Transactions on Cybernetics, vol. 48, no. 1, p. 240–252, 2018.
F. D. Kong and J. P. Sun, “Pinning synchronization of complex dynamical networks on time Scales,” International Journal of Control, Automation, and Systems, vol. 19, pp. 878–888, 2021.
F. Y. Liu, Y. Q. Yang, A. H. Hu, and L. Li, “Partial pinning control for the synchronization of fractional-order directed complex networks,” Neural Processing Letters, vol. 52, p. 1427–1444, 2020.
H. L. Yang, L. Shu, S. M. Zhong, T. Zhan, and X. Wang, “Pinning synchronization of stochastic T-S fuzzy delayed complex dynamical networks with heterogeneous impulsive delays,” International Journal of Control, Automation, and Systems, vol. 18, pp. 2599–2608, 2020.
D. Wang, W. W. Che, H. Yu, and J. Yang, “Adaptive pinning synchronization of complex networks with negative weights and its application,” International Journal of Control, Automation, and Sydtems, vol. 16, pp. 782–790, 2018.
H. Wang and Q. X. Zhu, “Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization,” Automatica, vol. 98, pp. 247–255, 2018.
Y. P. Luo, X. E. Wang, and J. D. Cao, “Guaranteed-cost finite-time consensus of multi-agent systems via intermittent control,” Mathematical Methods in the Applied Sciences, vol. 45, no. 1, pp. 697–717, 2022.
Q. Z. Wang, Y. He, G. Z. Tan, and M. Wu, “Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method,” Applied Mathematics and Computation, vol. 293, no. 15, pp. 438–447, 2017.
C. Ke, C. D. Li, Y. Y. Han, and L. You, “Adaptive fuzzy leader-following consensus for nonlinear multi-agent systems via state-constraint impulsive control,” International Journal of Machine Learning and Cybernetics, vol. 12, pp. 3011–3022, 2021.
Y. X. Lian, J. W. Xia, J. H. Park, W. Sun, and H. Shen, “Disturbance observer-based adaptive neural network output feedback control for uncertain nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 19, pp. 267–278, 2021.
Y. Liu, W. X. Li, K. W. Feng, and H. Song, “Periodically intermittent control for synchronized stationary distribution and synchronization of memristor-based stochastic coupled systems,” Transactions of the Institute of Measurement and Control, vol. 41, no. 14, pp. 4142–4156, 2019.
Q. Z. Wang and Y. He, “Time-triggered intermittent control of continuous systems,” Robust and Nonlinear Control, vol. 31, no. 14, pp. 6867–6879, 2021.
Z. L. Yan, X. Huang, and J. L. Liang, “Aperiodic sampleddata control for stabilization of memristive neural networks with actuator saturation: A dynamic partitioning method,” IEEE Transactions on Cybernetics, pp. 1–13, 2021. DOI: https://doi.org/10.1109/TCYB.2021.3108805
B. Ambrosio, M. A. Aziz-Alaoui, and V. L. E. Phan, “Large time behaviour and synchronization of complex networks of reaction-diffusion systems of fitzHugh-nagumo type,” IMA Journal of Applied Mathematics, vol. 84, no. 2, pp. 416–443, 2019.
L. Y. Cheng, F. C. Tang, X. L. Shi, X. Y. Chen, and J. L. Qiu, “Finite-time and fixed-time synchronization of delayed memristive neural networks via adaptive aperiodically intermittent adjustment strategy,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–15, 2022. DOI: https://doi.org/10.1109/TNNLS.2022.3151478
H. Shen, X. M. Liu, J. W. Xia, X. Y. Chen, and J. Wang, “Finite-time energy-to-peak fuzzy filtering for persistent dwell-time switched nonlinear systems with unreliable links,” Information Sciences, vol. 579, pp. 293–309, 2021.
J. Wang, T. T. Ru, H. Shen, J. D. Cao, and J. H. Park, “Finite-time \({{\cal L}_2} - {{\cal L}_\infty }\) synchronization for semi-Markov jump inertial neural networks using sampled data,” IEEE Transactions on Network Science and Engineering, vol. 8, no. 1, pp. 163–173, 2021.
L. Z. Zhang, J. Zhong, and J. Q. Lu, “Intermittent control for finite-time synchronization of fractional-order complex networks,” Neural Networks, vol. 144, pp. 11–20, 2021.
I. A. Darabsah and S. A. Campbell, “A phase model with large time delayed coupling,” Physica D: Nonlinear Phenomena, vol. 411, 132559, 2020.
H. Shen, S. Y. Jiao, J. H. Park, and V. Sreeram, “An improved result on H ∞ load frequency control for power systems with time delays,” IEEE Systems Journal, vol. 15, no. 3, pp. 3238–3248, 2021.
L. Yao, Z. Wang, X. Huang, Y. X. Li, Q. Ma, and H. Shen, “Stochastic sampled-data exponential synchronization of markovian jump neural networks with time-varying delays,” IEEE Transactions on Neral Networks And Learning Systems, vol. 34, no. 2, pp. 909–920, 2021.
Z. L. Yan, X. Huang, and J. D. Cao, “Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control,” Science China Information Sciences, vol. 63, 212201, 2020.
T. Y. Jing, D. Y. Zhang, J. Mei, and Y. Fan, “Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control,” Journal of the Franklin Institute, vol. 356, no. 10, p. 5464–5484, 2019.
T. Y. Jing and F. Q. Chen, “Finite-time lag synchronization of delayed neural networks via periodically intermittent control,” Complexity, vol. 21, pp. 211–219, 2016.
M. Liu, H. J. Jiang, and C. Hu, “Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control,” Journal of the Franklin Institute, vol. 354, no. 13, pp. 5374–5397, 2017.
J. W. Xia, Y. X. Lian, S. F. Su, H. Shen, and G. L. Chen, “Observer-based event-triggered adaptive fuzzy control for unmeasured stochastic nonlinear systems with unknown control directions,” IEEE Transactions on Cybernetics, vol. 52, no. 10 pp. 10655–10666, 2022.
Z. Tang, J. H. Park, and J. W. Feng, “Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 4, pp. 908–919, 2018.
N. Zhang, X. Y. Wang, and W. X. Li, “Stability for multi-linked stochastic delayed complex networks with stochastic hybrid impulses by Dupire Itô’s formula,” Nonlinear Analysis: Hybrid Systems, vol. 45, 101200, 2022.
Q. S. He and Y. C. Ma, “Quantized adaptive pinning control for fixed/preassigned-time cluster synchronization of multi-weighted complex networks with stochastic disturbances,” Nonlinear Analysis: Hybrid Systems, vol. 44, 101157, 2022.
S. Gao, C. Peng, J. X. Li, and C. R. Zhang, “Global asymptotic stability in mean for stochastic complex networked control systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 107, 106162, 2022.
X. L. He and H. Y. Zhang, “Exponential synchronization of complex networks via feedback control and periodically intermittent noise,” Journal of the Franklin Institute, vol. 359, no. 8, pp. 3614–3630, 2022.
H. Zhou, M. F. Luo, and W. X. Li, “Intermittent delay stabilization of complex-valued stochastic complex network,” Information Sciences, vol. 577, pp. 379–397, 2021.
X. L. Yuan, G. J. Ren, Y. G. Yu, and W. J. Sun, “Meansquare pinning control of fractional stochastic discrete-time complex networks,” Journal of the Franklin Institute, vol. 359, no. 6, pp. 2663–2680, 2022.
X. S. Yang and J. D. Cao, “Finite-time stochastic synchronization of complex networks,” Applied Mathematical Modelling, vol. 34, pp. 3631–3641, 2021.
X. J. Shi, Y. S. Zhao, and X. D. Li, “Finite-time synchronization for chaotic neural networks with stochastic disturbances,” Advances in Difference Equations, vol. 2020, 669, 2020.
T. L. Zhang and F. Q. Deng, “Adaptive finite-time synchronization of stochastic mixed time-varying delayed memristor-based neural networks,” Neurocomputing, vol. 452, pp. 781–788, 2021.
D. S. Xu, Y. Liu, and M. Liu, “Finite-time synchronization of multi-coupling stochastic fuzzy neural networks with mixed delays via feedback control,” Fuzzy Sets and Systems, vol. 411, pp. 85–104, 2021.
R. Sakthivel, F. Alzahrani, P. Selvaraj, and S. M. Anthoni, “Synchronization of complex dynamical networks with random coupling delay and actuator faults,” ISA Transactions, vol. 94, pp. 57–69, 2019.
L. L. Li, Z. W. Tu, J. Mei, and J. G. Jian, “Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods,” Nonlinear Dynamics, vol. 85, pp. 375–388, 2016.
X. W. Liu and T. P. Chen, “Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 10, pp. 2396–2407, 2015.
Q. Song and J. D. Cao, “On pinning synchronization of directed and undirected complex dynamical networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 3, pp. 672–680, 2010.
Y. L. Huang and F. Wu, “Finite-time passivity and synchronization of coupled complex-valued memristive neural networks,” Information Sciences, vol. 580, pp. 775–800, 2021.
M. Zhang, C. Shen, and Z. G. Wu, “Asynchronous observer-based control for exponential stabilization of Markov jump systems,” IEEE Transations on Circuits and Systems-II: Express Briefs, vol. 67, no. 10, pp. 2020–2039, 2020.
M. Zhang, P. Shi, C. Shen, and Z. G. Wu, “Static output feedback control of switched nonlinear systems with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 8, pp. 1600–1609, 2019.
X. P. Xie, C. Wei, Z. Gu, and K. B. Shi, “Relaxed resilient fuzzy stabilization of discrete-time takagi-sugeno systems via a higher order time-variant balanced matrix method,” IEEE Transactions on Fuzzy Systems, vol. 30, no. 11, pp. 5044–5050, 2022.
Author information
Authors and Affiliations
Corresponding author
Additional information
MingYu Wang is presently a master’s degree student in control engineering of Linyi University. Her research contents include synchronous control of complex networks and stochastic complex networks.
Feng Zhao was born in 1986. He graduated from Northeast University in 2015 with his doctorate in control science and engineering. In recent years, he has published more than 20 academic papers in academic journals and conferences at home and abroad. His research interests include nonlinear analysis (modeling and control and nonlinear dynamics).
JianLong Qiu was born in 1975. He received his doctorate degree in Southeast University in 2007. More than 100 highlevel papers have been published in international authoritative journals. The main research directions are logistics system optimization and control, logistics system design and development, complex network and complex system analysis and control, and neural network dynamics analysis.
XiangYong Chen was born in 1983. In 2012, he received a doctorate degree in control theory and control engineering from Northeast University. He has published dozens of papers on IEEE Transactions on automatic control, IEEE Transactions on cybernetics, and 8 highly cited papers on ESI. Mainly engaged in the analysis and control of complex networks and complex systems.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Thanks to Dr. Ming Guo for his help during the revision process of the article, including athe simulation analysis, the polishing of language, etc. The authors have declared that no conflict of interest exists.
Rights and permissions
About this article
Cite this article
Wang, M., Zhao, F., Qiu, J. et al. Adaptive Finite-time Synchronization of Stochastic Complex Networks with Mixed Delays via Aperiodically Intermittent Control. Int. J. Control Autom. Syst. 21, 1187–1196 (2023). https://doi.org/10.1007/s12555-022-0092-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-022-0092-x