\(H_\infty\) output synchronization of directed coupled reaction-diffusion neural networks via event-triggered quantized control. (English) Zbl 1465.93057
Summary: By designing a quantized controller based on event trigger, this paper considers the problem of \(H_\infty\) output synchronization for coupled neural networks with reaction-diffusion term and directed topology. Firstly, in this hybrid control strategy, the data is sampled in time domain to exclude the Zeno-behavior before judging whether an event is triggered, and then the event-triggered data instead of the sampling data itself is quantized by a logarithmic quantizer. Secondly, some sufficient conditions for \(H_\infty\) output synchronization are obtained, in which the dimension of these conditions can be reduced to only depend on the number of neurons, but not on the number of nodes. Finally, a numerical example is given to verify the theoretical results.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C65 | Discrete event control/observation systems |
| 93B70 | Networked control |
References:
| [1] | Chua, L.; Yang, L., Cellular neural networks: applications, IEEE Trans. Circuits Syst., 35, 10, 1273-1290 (1988) |
| [2] | Zhu, Q.; Cao, J., \(p\) th moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching, Nonlinear Dyn., 67, 829-845 (2012) · Zbl 1242.93126 |
| [3] | Zeng, Y.; Xiao, L.; Li, K.; Zuo, Q.; Li, K., Solving time-varying linear inequalities by finite-time convergent zeroing neural networks, J. Frankl. I., 357, 12, 8137-8155 (2020) · Zbl 1447.93319 |
| [4] | Chua, L.; Hasler, M.; Moschytz, G.; Neirynck, J., Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 42, 10, 559-577 (1995) |
| [5] | Hu, C.; Jiang, H.; Teng, Z., Exponential synchronization for reaction-diffusion networks with mixed delays in terms of \(p\)-norm via intermittent driving, Neural Netw., 31, 3, 1-11 (2012) · Zbl 1245.93122 |
| [6] | Rakkiyappan, R.; Dharani, S.; Zhu, Q., Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller, Nonlinear Dyn., 79, 1, 485-500 (2015) · Zbl 1331.92018 |
| [7] | Chen, W.; Luo, S.; Zheng, W., Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption, IEEE Trans. Neural Netw. Learn. Syst., 27, 12, 2696-2710 (2016) |
| [8] | Rao, R.; Zhong, S.; Pu, Z., Fixed point and \(p\)-stability of t-s fuzzy impulsive reaction-diffusion dynamic neural networks with distributed delay via laplacian semigroup, Neurocomputing, 335, 170-184 (2019) |
| [9] | Yang, X.; Cao, J.; Yang, Z., Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller, SIAM J. Control Optim., 51, 5, 3486-3510 (2013) · Zbl 1281.93052 |
| [10] | Rakkiyappan, R.; Dharani, S., Sampled-data synchronization of randomly coupled reaction-diffusion neural networks with markovian jumping and mixed delays using multiple integral approach, Neural Comput. Appl., 28, 3, 449-462 (2017) |
| [11] | Lu, B.; Jiang, H.; Hu, C.; Abdurahman, A., Synchronization of hybrid coupled reaction-diffusion neural networks with time delays via generalized intermittent control with spacial sampled-data, Neural Netw., 105, 75-87 (2018) · Zbl 1441.93247 |
| [12] | Hou, J.; Huang, Y.; Ren, S., Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms, Neurocomputing, 330, 78-93 (2019) |
| [13] | Huang, Y.; Hou, J.; Yang, E., General decay lag anti-synchronization of multi-weighted delayed coupled neural networks with reaction-diffusion terms, Inf. Sci., 511, 36-57 (2020) · Zbl 1460.92011 |
| [14] | Wang, J.; Wu, H.; Huang, T.; Ren, S.; Wu, J., Pinning control for synchronization of coupled reaction-diffusion neural networks with directed topologies, IEEE Trans. Syst Man Cybern. Syst., 46, 8, 1109-1120 (2016) |
| [15] | Zhang, H.; Sheng, Y.; Zeng, Z., Synchronization of coupled reaction-diffusion neural networks with directed topology via an adaptive approach, IEEE Trans. Neural Netw. Learn. Syst., 29, 5, 1550-1561 (2018) |
| [16] | Zhu, Q.; Wang, H., Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function, Automatica, 87, 166-175 (2018) · Zbl 1378.93141 |
| [17] | Yang, C.; Li, X.; Qiu, J., Output synchronization control with input constraint of complex networks with reaction-diffusion terms, Neural Comput. Appl., 30, 11, 3295-3302 (2018) |
| [18] | Suarez, O.; Vega, C.; Sanchez, E.; Chen, G., Neural sliding-mode pinning control for output synchronization for uncertain general complex networks, Automatica, 112, 108694 (2020) · Zbl 1430.93034 |
| [19] | Karimi, H.; Maass, P., Delay-range-dependent exponential \(h_\infty\) synchronization of a class of delayed neural networks, Chaos Soliton. Fract., 41, 3, 1125-1135 (2009) · Zbl 1198.93179 |
| [20] | Wu, K.; Chen, B., Synchronization of partial differential systems via diffusion coupling, IEEE Trans. Circuits Syst. I Reg. Pap., 59, 11, 2655-2668 (2012) · Zbl 1468.93085 |
| [21] | He, P.; Li, Y., \(h_\infty\) Synchronization of coupled reaction-diffusion neural networks with mixed delays, Complexity, 21, S2, 42-53 (2016) |
| [22] | Xu, Z.; Shi, P.; Su, H.; Wu, Z.; Huang, T., Global \(h_\infty\) pinning synchronization of complex networks with sampled-data communications, IEEE Trans. Neural Netw. Learn. Syst., 29, 5, 1467-1476 (2018) |
| [23] | Wang, J.; Wu, H.; Huang, T.; Xu, M., Output synchronization in coupled neural networks with and without external disturbances, IEEE Trans. Control Netw. Syst., 5, 4, 2049-2061 (2018) · Zbl 1515.93195 |
| [24] | Wang, J.; Qin, Z.; Wu, H.; Huang, T.; Wei, P., Analysis and pinning control for output synchronization and \(h_\infty\) output synchronization of multiweighted complex networks, IEEE Trans. Cybern., 49, 4, 1314-1326 (2019) · Zbl 1397.93006 |
| [25] | Lu, B.; Jiang, H.; Hu, C.; Abdurahman, A., Spacial sampled-data control for \(h_\infty\) output synchronization of directed coupled reaction-diffusion neural networks with mixed delays, Neural Netw., 123, 429-440 (2020) · Zbl 1443.93076 |
| [26] | Lu, W.; Han, Y.; Chen, T., Synchronization in networks of linearly coupled dynamical systems via event-triggered diffusions, IEEE Trans. Neural Netw. Learn. Syst., 26, 12, 3060-3069 (2015) |
| [27] | Arslan, E.; Vadivel, R.; Ali, M.; Arik, S., Event-triggered \(h_\infty\) filtering for delayed neural networks via sampled-data, Neural Netw., 91, 11-21 (2017) · Zbl 1441.93308 |
| [28] | Zhu, Q., Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control, IEEE Trans. Automat. Contr., 64, 9, 3764-3771 (2019) · Zbl 1482.93694 |
| [29] | Ali, M.; Vadivel, R.; Kwon, O., Decentralised event-triggered impulsive synchronisation for semi-markovian jump delayed neural networks with leakage delay and randomly occurring uncertainties, Int. J. Syst. Sci., 50, 5-8, 1636-1660 (2019) · Zbl 1483.93010 |
| [30] | Vadivel, R.; Ali, M.; Joo, Y., Drive-response synchronization of uncertain markov jump generalized neural networks with interval time varying delays via decentralized event-triggered communication scheme, J. Frankl. I., 357, 11, 6824-6857 (2020) · Zbl 1447.93363 |
| [31] | Ghodrat, M.; Marquez, H., On the local input-output stability of event-triggered control systems, IEEE T. Automat. Contr., 64, 1, 174-189 (2019) · Zbl 1423.93344 |
| [32] | Wang, A.; Liao, X.; Dong, T., Finite-time event-triggered synchronization for reaction-diffusion complex networks, Physica A, 509, 111-120 (2018) · Zbl 1514.93017 |
| [33] | Liberzon, D., Hybrid feedback stabilization of systems with quantized signals, Automatica, 39, 9, 1543-1554 (2003) · Zbl 1030.93042 |
| [34] | Wu, T.; Park, H.; Xiong, L.; Xie, X.; Zhang, H., A novel approach to synchronization conditions for delayed chaotic Lur’e systems with state sampled-data quantized controller, J. Frankl. I, 357, 14, 9811-9833 (2020) · Zbl 1448.93190 |
| [35] | Yang, X.; Song, Q.; Cao, J.; Lu, J., Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control, IEEE Trans. Neural Netw. Learn. Syst., 30, 3, 951-958 (2019) |
| [36] | Zhang, W.; Li, H.; Li, C.; Li, Z.; Yang, X., Fixed-time synchronization criteria for complex networks via quantized pinning control, ISA Trans., 91, 151-156 (2019) |
| [37] | Selivanov, A.; Fridman, E., Distributed event-triggered control of diffusion semilinear PDEs, Automatica, 68, 344-351 (2016) · Zbl 1334.93120 |
| [38] | Zheng, B.; Yu, X.; Xue, Y., Quantized feedback sliding-mode control: an event-triggered approach, Automatica, 91, 126-135 (2018) · Zbl 1387.93056 |
| [39] | Sun, M.; Huang, L.; Wang, S.; Mao, C.; Xie, W., Quantized control of event-triggered networked systems with time-varying delays, J. Frankl. I, 356, 17, 10368-10392 (2019) · Zbl 1425.93187 |
| [40] | Rakkiyappan, R.; Maheswari, K.; Velmurugan, G.; Park, J. H., Event-triggered \(h_\infty\) state estimation for semi-markov jumping discrete-time neural networks with quantization, Neural Netw., 105, 236-248 (2018) · Zbl 1441.93304 |
| [41] | Yu, W.; Chen, G.; Lü, J.; Kurths, J., Synchronization via pinning control on general complex networks, SIAM J. Control Optim., 51, 2, 1395-1416 (2013) · Zbl 1266.93071 |
| [42] | Girard, A., Dynamic triggering mechanisms for event-triggered control, IEEE T. Autom. Control, 60, 7, 1992-1997 (2013) · Zbl 1360.93423 |
| [43] | Ge, X.; Han, Q.; Ding, L.; Wang, Y.; Zhang, X., Dynamic event-triggered distributed coordination control and its applications: a survey of trends and techniques, IEEE Trans. Syst. Man Cybern. Syst., 50, 9, 3112-3125 (2020) |
| [44] | Dong, S.; Zhu, H.; Zhang, Y.; Zhong, S.; Cheng, J.; Shi, K., Design of \(h_\infty\) state estimator for delayed static neural networks under hybrid-triggered control and imperfect measurement strategy, J. Frankl. I, 357, 17, 13231-13257 (2020) · Zbl 1454.93059 |
| [45] | Cao, J.; Ding, D.; Liu, J.; Tian, E.; Hu, S.; Xie, X., Hybrid-triggered-based security controller design for networked control system under multiple cyber attacks, Inf. Sci., 548, 69-84 (2021) · Zbl 1478.93239 |
| [46] | Park, P.; Kob, J.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076 |
| [47] | Lu, W.; Chen, T., New approach to synchronization analysis of linearly coupled ordinary differential systems, Phys. D, 213, 2, 214-230 (2006) · Zbl 1105.34031 |
| [48] | Ali, M.; Vadivel, R.; Alsaedi, A.; Ahmad, B., Extended dissipativity and event-triggered synchronization for t-s fuzzy Markovian jumping delayed stochastic neural networks with leakage delays via fault-tolerant control, Soft Comput., 24, 3675-3694 (2020) · Zbl 1436.93004 |
| [49] | Rakkiyappan, R.; Latha, V.; Zhu, Q.; Yao, Z., Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators, Nonlinear Anal. Hybrid Syst., 24, 28-44 (2017) · Zbl 1377.93104 |
| [50] | Zhu, Q.; Cao, J., Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays, Commun. Nonlinear Sci. Numer. Simul., 16, 2139-2159 (2011) · Zbl 1221.93247 |
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