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Synchronization control of a class of memristor-based recurrent neural networks. (English) Zbl 1243.93049
Summary: In this paper, we formulate and investigate a class of memristor-based recurrent neural networks. Some sufficient conditions are obtained to guarantee the exponential synchronization of the coupled networks based on drive-response concept, differential inclusions theory and Lyapunov functional method. The analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. Finally, the validity of the obtained result is illustrated by a numerical example.
93C15Control systems governed by ODE
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93A14Decentralized systems
[1]Cao, J. D.; Li, L. L.: Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural netw. 22, 335-342 (2009)
[2]Cheng, C. J.; Liao, T. L.; Yan, J. J.; Hwang, C. C.: Exponential synchronization of a class of neural networks with time-varying delays, IEEE trans. Syst. man cybern. B, cybern. 36, 209-215 (2006)
[3]Chua, L. O.: Memristor-the missing circuit element, IEEE trans. Circuit theory 18, 507-519 (1971)
[4]Clarke, F. H.; Ledyaev, Y. S.; Stem, R. J.; Wolenski, R. R.: Nonsmooth analysis and control theory, (1998)
[5]Corinto, F.; Ascoli, A.; Gilli, M.: Nonlinear dynamics of memristor oscillators, IEEE trans. Circuits syst. I, reg. Pap. 58, 1323-1336 (2011)
[6]Cui, B. T.; Lou, X. Y.: Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control, Chaos solitons fract. 39, 288-294 (2009) · Zbl 1197.93135 · doi:10.1016/j.chaos.2007.01.100
[7]Doyle, J. C.; Glover, K.; Khargonekar, P. P.; Francis, B. A.: State-space solutions to standard H2 and H control problems, IEEE trans. Autom. control 34, 831-847 (1989) · Zbl 0698.93031 · doi:10.1109/9.29425
[8]Filippov, A. F.: Differential equations with discontinuous righthand sides, (1988)
[9]Gan, Q. T.; Xu, R.; Kang, X. B.: Synchronization of chaotic neural networks with mixed time delays, Comm. nonlinear sci. Numer. simul. 16, 966-974 (2011) · Zbl 1221.93222 · doi:10.1016/j.cnsns.2010.04.036
[10]Gao, X. Z.; Zhong, S. M.; Gao, F. Y.: Exponential synchronization of neural networks with time-varying delays, Nonlinear anal.: theory methods appl. 71, 2003-2011 (2009) · Zbl 1173.34349 · doi:10.1016/j.na.2009.01.243
[11]J. Hu, J. Wang, Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays, In: 2010 International Joint Conference on Neural Networks, IJCNN 2010, Barcelona, Spain, 2010, pp. 1 – 8.
[12]Huang, H.; Feng, G.: Synchronization of nonidentical chaotic neural networks with time delays, Neural netw. 22, 869-874 (2009)
[13]Huang, C. X.; He, Y. G.; Huang, L. H.; Zhu, W. J.: Pth moment stability analysis of stochastic recurrent neural networks with time-varying delays, Inform. sci. 178, 2194-2203 (2008) · Zbl 1144.93030 · doi:10.1016/j.ins.2008.01.008
[14]Itoh, M.; Chua, L. O.: Memristor oscillators, Int. J. Bifur. chaos 18, 3183-3206 (2008) · Zbl 1165.94300 · doi:10.1142/S0218127408022354
[15]Itoh, M.; Chua, L. O.: Memristor cellular automata and memristor discrete-time cellular neural networks, Int. J. Bifur. chaos 19, 3605-3656 (2009) · Zbl 1182.37014 · doi:10.1142/S0218127409025031
[16]Khalil, H. K.: Nonlinear systems, (1992) · Zbl 0969.34001
[17]Li, X. D.; Bohner, M.: Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback, Math. comput. Model. 52, 643-653 (2010) · Zbl 1202.34128 · doi:10.1016/j.mcm.2010.04.011
[18]Li, T.; Fei, S. M.; Zhang, K. J.: Synchronization control of recurrent neural networks with distributed delays, Phys. A: stat. Mech. appl. 387, 982-996 (2008)
[19]Li, T.; Fei, S. M.; Zhu, Q.; Cong, S.: Exponential synchronization of chaotic neural networks with mixed delays, Neurocomputing 71, 3005-3019 (2008)
[20]Li, T.; Song, A. G.; Fei, S. M.; Guo, Y. Q.: Synchronization control of chaotic neural networks with time-varying and distributed delays, Nonlinear anal.: theory methods appl. 71, 2372-2384 (2009) · Zbl 1171.34049 · doi:10.1016/j.na.2009.01.079
[21]Liu, M. Q.: Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach, Neural netw. 22, 949-957 (2009)
[22]Liu, B.; Lu, W. L.; Chen, T. P.: Global almost sure self-synchronization of Hopfield neural networks with randomly switching connections, Neural netw. 24, 305-310 (2011) · Zbl 1225.93019 · doi:10.1016/j.neunet.2010.12.005
[23]Lou, X. Y.; Cui, B. T.: Synchronization of neural networks based on parameter identification and via output or state coupling, J. appl. Math. comput. 222, 40-457 (2008) · Zbl 1168.65041 · doi:10.1016/j.cam.2007.11.015
[24]Lu, J. G.; Chen, G. R.: Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: an LMI approach, Chaos solitons fract. 41, 2293-2300 (2009) · Zbl 1198.37141 · doi:10.1016/j.chaos.2008.09.024
[25]Lu, Z.; Shieh, L. S.; Chen, G. R.; Coleman, N. P.: Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks, Inform. sci. 176, 2337-2354 (2006) · Zbl 1116.93035 · doi:10.1016/j.ins.2005.08.002
[26]Merrikh-Bayat, F.; Shouraki, S. B.: Memristor-based circuits for performing basic arithmetic operations, Procedia comput. Sci. 3, 128-132 (2011)
[27]Michel, A. N.; Hou, L.; Liu, D.: Stability of dynamical systems: continuous, Discontinuous and discrete systems (2007)
[28]Petras, I.: Fractional-order memristor-based Chua’s circuit, IEEE trans. Circuits syst. II, exp. Briefs 57, 975-979 (2010)
[29]Posadas-Castillo, C.; Cruz-Hernandez, C.; Lopez-Gutierrez, R. M.: Synchronization of chaotic neural networks with delay in irregular networks, Appl. math. Comput. 205, 487-496 (2008) · Zbl 1184.34081 · doi:10.1016/j.amc.2008.08.015
[30]Sanchez, E. N.; Ricalde, L. J.: Chaos control and synchronization, with input saturation, via recurrent neural networks, Neural netw. 16, 711-717 (2003)
[31]Sheng, L.; Yan, H. Z.: Exponential synchronization of a class of neural networks with mixed time-varying delays and impulsive effects, Neurocomputing 71, 3666-3674 (2008)
[32]Song, Q. K.: Synchronization analysis of coupled connected neural networks with mixed time delays, Neurocomputing 72, 3907-3914 (2009)
[33]Song, Q. K.: Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling, Appl. math. Comput. 216, 1605-1613 (2010) · Zbl 1194.34145 · doi:10.1016/j.amc.2010.03.014
[34]Strukov, D. B.; Snider, G. S.; Stewart, G. R.; Williams, R. S.: The missing memristor found, Nature 453, 80-83 (2008)
[35]Tour, J. M.; He, T.: The fourth element, Nature 453, 42-43 (2008)
[36]Wu, A. L.; Fu, C. J.: Global exponential stability of non-autonomous fcnns with Dirichlet boundary conditions and reaction-diffusion terms, Appl. math. Model. 34, 3022-3029 (2010) · Zbl 1201.35049 · doi:10.1016/j.apm.2010.01.010
[37]Wu, A. L.; Zeng, Z. G.; Fu, C. J.; Shen, W. W.: Global exponential stability in Lagrange sense for periodic neural networks with various activation functions, Neurocomputing 74, 831-837 (2011)
[38]Yang, X. S.; Cao, J. D.: Stochastic synchronization of coupled neural networks with intermittent control, Phys. lett. A 373, 3259-3272 (2009) · Zbl 1233.34020 · doi:10.1016/j.physleta.2009.07.013
[39]Yoo, S. J.; Park, J. B.; Choi, Y. H.: Indirect adaptive control of nonlinear dynamic systems using self-recurrent wavelet neural networks via adaptive learning rates, Inform. sci. 177, 3074-3098 (2007) · Zbl 1120.93329 · doi:10.1016/j.ins.2007.02.009
[40]Yu, W. W.; Cao, J. D.; Lu, W. L.: Synchronization control of switched linearly coupled neural networks with delay, Neurocomputing 73, 858-866 (2010)
[41]Zeng, Z. G.; Wang, J.: Analysis and design of associative memories based on recurrent neural networks with linear saturation activation functions and time-varying delays, Neural comput. 19, 2149-2182 (2007) · Zbl 1143.68569 · doi:10.1162/neco.2007.19.8.2149
[42]Zhang, C. K.; He, Y.; Wu, M.: Exponential synchronization of neural networks with time-varying mixed delays and sampled-data, Neurocomputing 74, 265-273 (2010)
[43]Zhang, Y. P.; Sun, J. T.: Robust synchronization of coupled delayed neural networks under general impulsive control, Chaos solitons fract. 41, 1476-1480 (2009) · Zbl 1198.34129 · doi:10.1016/j.chaos.2008.06.010