Practical synchronization of neural networks with delayed impulses and external disturbance via hybrid control. (English) Zbl 1525.93422
Summary: This paper studies the problem of practical synchronization for delayed neural networks via hybrid-driven impulsive control in which delayed impulses and external disturbance are taken into account. Firstly, a switching method which establishes the relationship between error signals and a threshold function is introduced, which determines whether time-driven control or event-driven control is activated. Secondly, the effects of delayed impulses and external disturbance on impulsive systems are considered, and the corresponding comparison lemma is proposed. Thirdly, whenever the norm of the initial value of the error system state is less than or greater than the initial value of the threshold function, under the proposed hybrid-driven impulsive control scheme, the practical synchronization of the delayed neural networks with delayed impulses and external disturbance can be achieved by synchronizing impulses. Moreover, the Zeno behavior can be excluded under the proposed hybrid-driven impulsive control. Finally, two numerical examples are presented to verify the effectiveness of the theoretical results.
MSC:
| 93D99 | Stability of control systems |
| 93C27 | Impulsive control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C73 | Perturbations in control/observation systems |
| 93B70 | Networked control |
| 93C43 | Delay control/observation systems |
Keywords:
neural networks; practical synchronization; hybrid-driven impulsive control; delayed impulses; external disturbanceReferences:
| [1] | Chen, J.; Park, J. H.; Xu, S., Improved stability criteria for discrete-time delayed neural networks via novel Lyapunov-Krasovskii functionals, IEEE Transactions on Cybernetics (2021) |
| [2] | Chen, W.-H.; Zheng, W. X., Exponential stability of nonlinear time-delay systems with delayed impulse effects, Automatica, 47, 5, 1075-1083 (2011) · Zbl 1233.93080 |
| [3] | Ding, S.; Wang, Z.; Rong, N.; Zhang, H., Exponential stabilization of memristive neural networks via saturating sampled-data control, IEEE Transactions on Cybernetics, 47, 10, 3027-3039 (2017) |
| [4] | Ding, S.; Wang, Z.; Zhang, H., Event-triggered control for a class of non-linear systems: An exponential approximation method, IET Control Theory & Applications, 12, 10, 1491-1496 (2018) |
| [5] | Ding, S.; Wang, Z.; Zhang, H., Quasi-synchronization of delayed memristive neural networks via region-partitioning-dependent intermittent control, IEEE Transactions on Cybernetics, 49, 12, 4066-4077 (2018) |
| [6] | Dong, S.; Zhu, H.; Zhong, S.; Shi, K.; Lu, J., Impulsive-based almost surely synchronization for neural network systems subject to deception attacks, IEEE Transactions on Neural Networks and Learning Systems (2021) |
| [7] | Feldkamp, L.; Puskorius, G., A signal processing framework based on dynamic neural networks with application to problems in adaptation, filtering, and classification, Proceedings of the IEEE, 86, 11, 2259-2277 (1998) |
| [8] | Gosak, M.; Markovič, R.; Dolenšek, J.; Slak Rupnik, M.; Marhl, M.; Stožer, A., Network science of biological systems at different scales: A review, Physics of Life Reviews, 24, 118-135 (2018) |
| [9] | Gosak, M.; Milojević, M.; Duh, M.; Skok, K.; Perc, M., Networks behind the morphology and structural design of living systems, Physics of Life Reviews, 41, 1-21 (2022) |
| [10] | He, W.; Qian, F.; Cao, J., Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Networks, 85, 1-9 (2017) · Zbl 1429.93351 |
| [11] | Hu, T.; Liu, X.; He, Z.; Zhang, X.; Zhong, S., Hybrid event-triggered and impulsive control strategy for multiagent systems with switching topologies, IEEE Transactions on Cybernetics, 52, 7, 6283-6294 (2022) |
| [12] | Hu, T.; Park, J. H.; Liu, X.; He, Z.; Zhong, S., Sampled-data-based event-triggered synchronization strategy for fractional and impulsive complex networks with switching topologies and time-varying delay, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52, 6, 3568-3580 (2022) |
| [13] | Hu, M.-J.; Park, J. H.; Wang, Y.-W., Stabilization of positive systems with time delay via the Takagi-Sugeno fuzzy impulsive control, IEEE Transactions on Cybernetics, 52, 6, 4275-4285 (2022) |
| [14] | Khadra, A.; Liu, X.; Shen, X., Impulsively synchronizing chaotic systems with delay and applications to secure communication, Automatica, 41, 9, 1491-1502 (2005) · Zbl 1086.93051 |
| [15] | Kim, J.; Hastak, M., Social network analysis: Characteristics of online social networks after a disaster, International Journal of Information Management, 38, 1, 86-96 (2018) |
| [16] | Lakshmikantham, V.; Leela, S.; Martynyuk, A., Practical stability of nonlinear systems (1990), World Scientific · Zbl 0753.34037 |
| [17] | Lehmann, D.; Lunze, J., Event-based output-feedback control, (2011 19th Mediterranean conference on control & automation (2011)), 982-987 |
| [18] | Li, X.; Ho, D. W.; Cao, J., Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99, 361-368 (2019) · Zbl 1406.93260 |
| [19] | Li, X.; Peng, D.; Cao, J., Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Transactions on Automatic Control, 65, 11, 4908-4913 (2020) · Zbl 1536.93638 |
| [20] | Li, X.; Yang, X.; Cao, J., Event-triggered impulsive control for nonlinear delay systems, Automatica, 117, Article 108981 pp. (2020) · Zbl 1441.93179 |
| [21] | Li, M.; Yang, X.; Li, X., Delayed impulsive control for lag synchronization of delayed neural networks involving partial unmeasurable states, IEEE Transactions on Neural Networks and Learning Systems (2022) |
| [22] | Li, X.; Zhu, H.; Song, S., Input-to-state stability of nonlinear systems using observer-based event-triggered impulsive control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 11, 6892-6900 (2021) |
| [23] | Liu, X.; Zhang, K., Stabilization of nonlinear time-delay systems: Distributed-delay dependent impulsive control, Systems & Control Letters, 120, 17-22 (2018) · Zbl 1408.93113 |
| [24] | Lu, J.; Ho, D. W.; Cao, J., A unified synchronization criterion for impulsive dynamical networks, Automatica, 46, 7, 1215-1221 (2010) · Zbl 1194.93090 |
| [25] | Lu, J.; Ho, D. W.; Cao, J.; Kurths, J., Exponential synchronization of linearly coupled neural networks with impulsive disturbances, IEEE Transactions on Neural Networks, 22, 2, 329-336 (2011) |
| [26] | Lu, J.; Kurths, J.; Cao, J.; Mahdavi, N.; Huang, C., Synchronization control for nonlinear stochastic dynamical networks: Pinning impulsive strategy, IEEE Transactions on Neural Networks and Learning Systems, 23, 2, 285-292 (2011) |
| [27] | Lunze, J.; Lehmann, D., A state-feedback approach to event-based control, Automatica, 46, 1, 211-215 (2010) · Zbl 1213.93063 |
| [28] | Petersen, I. R.; Hollot, C. V., A Riccati equation approach to the stabilization of uncertain linear systems, Automatica, 22, 4, 397-411 (1986) · Zbl 0602.93055 |
| [29] | Shanmugam, L.; Mani, P.; Rajan, R.; Joo, Y. H., Adaptive synchronization of reaction-diffusion neural networks and its application to secure communication, IEEE Transactions on Cybernetics, 50, 3, 911-922 (2018) |
| [30] | Shen, H.; Jiao, S.; Cao, J.; Huang, T., An improved result on sampled-data synchronization of Markov jump delayed neural networks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 6, 3608-3616 (2021) |
| [31] | Shen, Y.; Liu, X., Event-based master-slave synchronization of complex-valued neural networks via pinning impulsive control, Neural Networks, 145, 374-385 (2022) · Zbl 1526.93162 |
| [32] | Shen, H.; Wang, X.; Wang, J.; Cao, J.; Rutkowski, L., Robust composite \(H_\infty\) synchronization of Markov jump reaction-diffusion neural networks via a disturbance observer-based method, IEEE Transactions on Cybernetics (2021) |
| [33] | Tang, Z.; Park, J. H.; Feng, J., Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay, IEEE Transactions on Neural Networks and Learning Systems, 29, 4, 908-919 (2017) |
| [34] | Tian, Y.; Wang, Z., Stochastic stability of Markovian neural networks with generally hybrid transition rates, IEEE Transactions on Neural Networks and Learning Systems (2021) |
| [35] | Wang, Q.; He, Y.; Tan, G.; Wu, M., State-dependent intermittent control of non-linear systems, IET Control Theory & Applications, 11, 12, 1884-1893 (2017) |
| [36] | Wang, N.; Li, X.; Lu, J.; Alsaadi, F. E., Unified synchronization criteria in an array of coupled neural networks with hybrid impulses, Neural Networks, 101, 25-32 (2018) · Zbl 1441.93256 |
| [37] | Wang, Q.; Perc, M.; Duan, Z.; Chen, G., Synchronization transitions on scale-free neuronal networks due to finite information transmission delays, Physical Review E, 80, Article 026206 pp. (2009) |
| [38] | Wang, Q.; Perc, M.; Duan, Z.; Chen, G., Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling, Physica A, 389, 16, 3299-3306 (2010) |
| [39] | Wang, F.; Sun, Y., Self-organizing peer-to-peer social networks, Computational Intelligence, 24, 3, 213-233 (2008) |
| [40] | Xie, W.; Zhu, H.; Cheng, J.; Zhong, S.; Shi, K., Finite-time asynchronous \(H_\infty\) resilient filtering for switched delayed neural networks with memory unideal measurements, Information Sciences, 487, 156-175 (2019) · Zbl 1454.93253 |
| [41] | Yang, X.; Lu, J., Finite-time synchronization of coupled networks with Markovian topology and impulsive effects, IEEE Transactions on Automatic Control, 61, 8, 2256-2261 (2016) · Zbl 1359.93459 |
| [42] | Zhang, J.; Feng, G., Event-driven observer-based output feedback control for linear systems, Automatica, 50, 7, 1852-1859 (2014) · Zbl 1296.93117 |
| [43] | Zhao, C.; Zhong, S.; Zhang, X.; Zhong, Q.; Shi, K., Novel results on nonfragile sampled-data exponential synchronization for delayed complex dynamical networks, International Journal of Robust and Nonlinear Control, 30, 10, 4022-4042 (2020) · Zbl 1466.93133 |
| [44] | Zhou, Y.; Zeng, Z., Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays, Neural Networks, 110, 55-65 (2019) · Zbl 1441.93188 |
| [45] | Zhou, Y.; Zhang, H.; Zeng, Z., Quasi-synchronization of delayed memristive neural networks via a hybrid impulsive control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 3, 1954-1965 (2021) |
| [46] | Zhu, W.; Wang, D.; Liu, L.; Feng, G., Event-based impulsive control of continuous-time dynamic systems and its application to synchronization of memristive neural networks, IEEE Transactions on Neural Networks and Learning Systems, 29, 8, 3599-3609 (2017) |
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