×

Analysis of adaptive synchronization for stochastic neutral-type memristive neural networks with mixed time-varying delays. (English) Zbl 1417.93168

Summary: Linear feedback control and adaptive feedback control are proposed to achieve the synchronization of stochastic neutral-type memristive neural networks with mixed time-varying delays. By applying the stochastic differential inclusions theory, Lyapunov functional, and linear matrix inequalities method, we obtain some new adaptive synchronization criteria. A numerical example is given to illustrate the effectiveness of our results.

MSC:

93C40 Adaptive control/observation systems
92B20 Neural networks for/in biological studies, artificial life and related topics
93E03 Stochastic systems in control theory (general)
34K20 Stability theory of functional-differential equations

References:

[1] Zhang, Z.; Liu, W.; Zhou, D., Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays, Neural Networks, 25, 94-105 (2012) · Zbl 1266.34124 · doi:10.1016/j.neunet.2011.07.006
[2] Zeng, X.; Xiong, Z.; Wang, C., Hopf bifurcation for neutral-type neural network model with two delays, Applied Mathematics and Computation, 282, 17-31 (2016) · Zbl 1410.37087 · doi:10.1016/j.amc.2016.01.050
[3] Du, B.; Zhang, W.; Yang, Q., Robust state estimation for neutral-type neural networks with mixed time delays, Journal of Nonlinear Sciences and Applications. JNSA, 10, 5, 2565-2578 (2017) · Zbl 1412.34085 · doi:10.22436/jnsa.010.05.24
[4] Chua, L. O., Memristor—the missing circuit element, IEEE Transactions on Circuit Theory, 18, 5, 507-519 (1971) · doi:10.1109/TCT.1971.1083337
[5] Strukov, D. B.; Snider, G. S.; Stewart, D. R.; Williams, R. S., The missing memristor found, Nature, 453, 80-83 (2008) · doi:10.1038/nature06932
[6] 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) · doi:10.1109/TCYB.2017.2711496
[7] Cantley, K. D.; Subramaniam, A.; Stiegler, H. J.; Chapman, R. A.; Vogel, E. M., Neural learning circuits utilizing nano-crystalline silicon transistors and memristors, IEEE Transactions on Neural Networks and Learning Systems, 23, 4, 565-573 (2012) · doi:10.1109/TNNLS.2012.2184801
[8] Zhu, Q.; Cao, J., Pth moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching, Nonlinear Dynamics, 67, 1, 829-845 (2012) · Zbl 1242.93126 · doi:10.1007/s11071-011-0029-z
[9] Rakkiyappan, R.; Dharani, S.; Zhu, Q., Stochastic sampled-data \(H_∞\) synchronization of coupled neutral-type delay partial differential systems, Journal of The Franklin Institute, 352, 10, 4480-4502 (2015) · Zbl 1395.93359 · doi:10.1016/j.jfranklin.2015.06.019
[10] Li, X.; Fang, J. A.; Li, H., Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays, Neurocomputing, 267, 396-405 (2017) · doi:10.1016/j.neucom.2017.06.049
[11] Rakkiyappan, R.; Dharani, S.; Zhu, Q., Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller, Nonlinear Dynamics, 79, 1, 485-500 (2015) · Zbl 1331.92018 · doi:10.1007/s11071-014-1681-x
[12] Ding, S.; Wang, Z., Stochastic exponential synchronization control of mem-ristive neural networks with multiple time-varying delays, Neurocomputing, 162, 16-25 (2015) · doi:10.1016/j.neucom.2015.03.069
[13] Ding, S.; Wang, Z.; Wang, J.; Zhang, H., \(H_∞\) State estimation for memristive neural networks with time-varying delays: The discrete-time case, Neural Networks, Neural Networks, 84, 47-56 (2016) · Zbl 1429.93365 · doi:10.1016/j.neunet.2016.08.002
[14] Zhang, C.; Deng, F.; Zhao, X.; Zhang, B., p-th exponential synchronization of Cohen-Grossberg neural network with mixed time-varying delays and unknown parameters using impulsive control method, Neurocomputing, 218, 432-438 (2016) · doi:10.1016/j.neucom.2016.09.002
[15] Zhu, Q.; Cao, J., Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays, Nonlinear Dynamics, 61, 3, 517-534 (2010) · Zbl 1204.93064 · doi:10.1007/s11071-010-9668-8
[16] Gao, J.; Zhu, P.; Xiong, W.; Cao, J.; Zhang, L., Asymptotic synchronization for stochastic memristor-based neural networks with noise disturbance, Journal of The Franklin Institute, 353, 13, 3271-3289 (2016) · Zbl 1344.93090 · doi:10.1016/j.jfranklin.2016.06.002
[17] Du, B.; Hu, M.; Lian, X., Dynamical behavior for a stochastic predator-prey model with {HV} type functional response, Bulletin of the Malaysian Mathematical Sciences Society, 40, 1, 487-503 (2017) · Zbl 1358.34091 · doi:10.1007/s40840-016-0325-3
[18] Liu, D.; Du, Y., New results of stability analysis for a class of neutral-type neural network with mixed time delays, Proceedings of the International Journal of Machine Learning Cybernetics 6 (4
[19] Du, B.; Liu, Y.; Cao, D., Stability analysis for neutral-type impulsive neural networks with delays, Kybernetika, 53, 3, 513-529 (2017) · Zbl 1424.34246 · doi:10.14736/kyb-2017-3-0513
[20] Ding, S.; Wang, Z.; Niu, H.; Zhang, H., Stop and go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights, Journal of The Franklin Institute, 354, 12, 4989-5010 (2017) · Zbl 1367.93303 · doi:10.1016/j.jfranklin.2017.05.011
[21] Chandrasekar, A.; Rakkiyappan, R., Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks, Neurocomputing, 173, 1348-1355 (2016) · doi:10.1016/j.neucom.2015.08.088
[22] Wang, T.; Gao, H.; Qiu, J., A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control, IEEE Transactions on Neural Networks and Learning Systems, 99 (2015) · doi:10.1109/TNNLS.2015.2411671
[23] Ding, S.; Wang, Z.; Huang, Z.; Zhang, H., Novel switching jumps dependent exponential synchronization criteria for memristor-based neural networks, Neural Processing Letters, 45, 1, 15-28 (2017) · doi:10.1007/s11063-016-9504-3
[24] Zhang, G.; Hu, J.; Shen, Y., Exponential lag synchronization for delayed memristive recurrent neural networks, Neurocomputing, 154, 86-93 (2015) · doi:10.1016/j.neucom.2014.12.016
[25] Rakkiyappan, R.; Preethi Latha, V.; Zhu, Q.; Yao, Z., Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators, Nonlinear Analysis: Hybrid Systems, 24, 28-44 (2017) · Zbl 1377.93104 · doi:10.1016/j.nahs.2016.10.004
[26] Chen, C.; Li, L.; Peng, H.; Yang, Y.; Li, T., Finite-time synchronization of memristor-based neural networks with mixed delays, Neurocomputing, 235, 83-89 (2017) · doi:10.1016/j.neucom.2016.12.061
[27] Zhu, Q.; Cao, J., Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays, Communications in Nonlinear Science & Numerical Simulation, 16, 4, 2139-2159 (2011) · Zbl 1221.93247 · doi:10.1016/j.cnsns.2010.08.037
[28] Zhu, Q.; Cao, J., Stability of Markovian jump neural networks with impulse control and time varying delays, Nonlinear Analysis: Real World Applications, 13, 5, 2259-2270 (2012) · Zbl 1254.93157 · doi:10.1016/j.nonrwa.2012.01.021
[29] Zhu, Q.; Cao, J., Stability analysis of markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Transactions on Neural Networks and Learning Systems, 23, 3, 467-479 (2012) · doi:10.1109/TNNLS.2011.2182659
[30] Zhu, Q.; Cao, J., Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41, 2, 341-353 (2011) · doi:10.1109/TSMCB.2010.2053354
[31] Zhu, Q.; Zhou, W.; Tong, D.; Fang, J., Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays, Neurocomputing, 99, 477-485 (2013) · doi:10.1016/j.neucom.2012.07.013
[32] Liao, X.; Chen, G.; Sanchez, E. N., L{MI}-based approach for asymptotically stability analysis of delayed neural networks, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49, 7, 1033-1039 (2002) · Zbl 1368.93598 · doi:10.1109/TCSI.2002.800842
[33] Gu, K., An integral inequality in the stability problem of time-delay systems, Proceedings of the Proceedings of the 39th IEEE Confernce on Decision and Control
[34] Peng, W.; Wu, Q.; Zhang, Z., LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique, Neurocomputing, 199, 103-113 (2016) · doi:10.1016/j.neucom.2016.03.030
[35] Yaz, E., Linear Matrix Inequalities In System And Control Theory, Proceedings of the IEEE, 86, 12, 2473-2474 (1998) · doi:10.1109/JPROC.1998.735454
[36] Mao, X., A note on the LaSalle-type theorems for stochastic differential delay equations, Journal of Mathematical Analysis and Applications, 268, 1, 125-142 (2002) · Zbl 0996.60064 · doi:10.1006/jmaa.2001.7803
[37] Wang, W.; Li, L.; Peng, H.; Wang, W.; Kurths, J.; Xiao, J.; Yang, Y., Anti-synchronization of coupled memristive neutral-type neural networks with mixed time-varying delays via randomly occurring control, Nonlinear Dynamics, 83, 4, 2143-2155 (2016) · Zbl 1353.92010 · doi:10.1007/s11071-015-2471-9
[38] Zhang, C.; Deng, F.; Peng, Y.; Zhang, B., Adaptive synchronization of Cohen-Grossberg neural network with mixed time-varying delays and stochastic perturbation, Applied Mathematics and Computation, 269, 792-801 (2015) · Zbl 1410.92015 · doi:10.1016/j.amc.2015.07.074
[39] Gan, Q., Adaptive synchronization of cohen-grossberg neural networks with unknown parameters and mixed time-varying delays â \(˜\)†, Communications in Nonlinear Science and Numerical Simulation, 17, 7, 3040-3049 (2012) · Zbl 1243.93054 · doi:10.1016/j.cnsns.2011.11.012
[40] Wang, X.; She, K.; Zhong, S.; Cheng, J., Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation, Neurocomputing, 242, 131-139 (2017) · doi:10.1016/j.neucom.2017.02.059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.