Abstract
In this paper, the problem of the adaptive synchronization control is considered for neural networks with uncertainty and stochastic noise. Via utilizing stochastic analysis method and linear matrix inequality (LMI) approach, several sufficient conditions to ensure the adaptive synchronization for neural networks are derived. By the adaptive feedback methods, some suitable parameters update laws are found. Finally, a simulation result is provided to substantiate the effectiveness of the proposed approach.
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W. Feng, S. X. Yang, and H. Wu, “Further results on robust stability of bidirectional associative memory neural networks with norm-bounded uncertainties,” Neurocomputing, vol. 148, pp. 535–543, 2015. [click]
N. Kasabov, K. Dhoble, N. Nuntalid, and G. Indiveri, “Dynamic evolving spiking neural networks for on-line spatioand spectro-temporal pattern recognition,” Neural Netw., vol. 41, pp. 188–201, 2013. [click]
X. Liu, S. Zhong, and X. Ding, “Robust exponential stability of impulsive switched systems with switching delays: a razumikhin approach,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 4, pp. 1805–1812, 2012. [click]
Z. Wang and H. Zhang, “Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays,” IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 39–49, 2010. [click]
P. Balasubramaniam, S. Lakshmanan, and R. Rakkiyappan, “LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties,” Int. J. Appl. Math. Comput. Sci., vol. 22, no. 2, pp. 339–351, 2012. [click]
W. Zhou, D. Tong, Y. Gao, C. Ji, and H. Su, “Mode and delay-dependent adaptive exponential synchronization in pth moment for stochastic delayed neural networks with Markovian switching,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 4, pp. 662–668, 2012. [click]
Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 9, pp. 1368–1376, 2012. [click]
D. Tong, W. Zhou, and H. Wang, “Exponential state estimation for stochastic complex dynamical networks with multi-delayed base on adaptive control,” Int J. Control Autom. Syst., vol. 12, no. 5, pp. 963–968, 2014. [click]
H. Li, “Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling.” Neurocomputing, vol. 138, pp. 78–85, 2014. [click]
Q. Zhu and J. Cao, “Adaptive synchronization under almost every initial data for stochastic neural networks with timevarying delays and distributed delays,” Commun. Nonlinear Sci. Numer. Simulat. vol. 16, no. 4, pp. 2139–2159, 2011. [click]
W. Yu, J. Cao, and W. Lu, “Synchronization control of switched linearly coupled neural networks with delay,” Neurocomputing, vol. 73, no. 4, pp. 858–866, 2010. [click]
D. Tong, W. Zhou, X. Zhou, J. Yang, L. Zhang, and Y. Xu. Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control. Commun. Nonlinear Sci. Numer. Simulat., vol. 29, no. 5, pp. 359–371, 2015.
J. Lu, J. Kurths, J. Cao, N. Mahdavi, and C. Huang, “Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 285–292, 2012. [click]
M. Liu, H. Chen, S. Zhang, and W. Sheng, “H ∞ synchronization of two different discrete-time chaotic systems via a unified model,” Int. J. Control Autom. Syst., vol. 13, no. 1, pp. 212–221, 2015. [click]
H. Li, “H ∞ cluster synchronization and state estimation for complex dynamical networks with mixed time delays,” Appl. Math. Model., vol. 37, no. 12, pp. 7223–7244, 2013. [click]
Q. Gan, R. Hu, and Y. Liang, “Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 9, pp. 3708–3718, 2012.
D. Tong, Q. Zhu, W. Zhou, Y. Xu, and J. Fang, “Adaptive synchronization for stochastic T-S fuzzy neural networks with time-delay and Markovian jumping parameters,” Neurocomputing, vol. 117, no. 1, pp. 91–97, 2013. [click]
Y. Tang, H. Gao, and J. Kurths, “Distributed robust synchronization of dynamical networks with stochastic coupling,” IEEE Trans. Circuits Syst. Regul. Pap., vol. 61, no. 5, pp. 1508–1519, 2014. [click]
R. Lu, W. Yu, J. Lu, and A. Xue, “Synchronization on complex networks of networks,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 11, pp. 2110–2118, 2014. [click]
C. Yuan and X. Mao, “Robust stability and controllability of stochastic differential delay equations with Markovian switching,” Automatica, vol. 40, no. 3, pp. 343–354, 2004. [click]
X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, World Scientific, 2006.
D. Tong, W. Zhou, Y. Gao, C. Ji, and H. Su, “H ∞ model reduction for port-controlled Hamiltonian systems,” Appl. Math. Model., vol. 37, no. 5, pp. 2727–2736, 2013. [click]
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Recommended by Editor Ju Hyun Park. This work was supported by the National Natural Science Foundation of China (11501367), the Chinese Postdoctoral Science Foundation (2015M581528), the Natural Science Foundation of Shanghai (15ZR1419000, 15ZR1401800), the Young Teacher Training Scheme of Shanghai Universities (ZZGCD15004, ZZLX15031), Doctoral Starting Foundation of Shanghai University of Engineering Science (Xiaoqi 2015-21), the Youth Fund Project of the Humanities and Social Science Research for the Ministry of Education of China (14YJCZH173), the Science and Technology Research Key Program for the Education Department of Hubei Province of China (D20155001, D20156001), and the Science and Technology Research Youth Project for the Education Department of Hubei Province of China (Q20145001).
Dongbing Tong received his Ph.D. degree in Control Theory and Control Engineering from Donghua University, Shanghai, China, in 2014. He is currently a Lecturer at Shanghai University of Engineering Science, Shanghai, China. His current research interests include complex networks, and model reduction.
Liping Zhang received his M.S. degree in Control Theory and Control Engineering from Donghua University, Shanghai, China, in 2010. She is currently a Professor at Shanghai University of Engineering Science, Shanghai, China. Her current research interests include communication system, and detection system.
Wuneng Zhou received a first class B.S. degree from Huazhong Normal University in 1982. He obtained his Ph.D. degree from Zhejiang University in 2005. Now he is a professor in Donghua University, Shanghai. His current research interests include the stability, the synchronization, control of neural networks and complex networks.
Jun Zhou received the M.S. degree in computer application technology from Yunnan University, Yunnan, China, in 2010. Now he is under a Ph.D. candidate in control science and engineering form Donghua University, Shanghai and a teacher in Southwest Forestry University, Yunnan, China. His current research interests include the stability, the synchronization and control for neural networks.
Yuhua Xu received his Ph.D. degree in Control Theory and Control Engineering from Donghua University, P. R. China in 2011. Currently he is a Professor at Nanjing Audit University. His research interests include the network control, nonlinear finance systems, dynamics and control.
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Tong, D., Zhang, L., Zhou, W. et al. Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control. Int. J. Control Autom. Syst. 14, 706–712 (2016). https://doi.org/10.1007/s12555-015-0077-0
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DOI: https://doi.org/10.1007/s12555-015-0077-0