A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 3 Issue 2
Apr.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2016  >  3(2): 121-131
Zhenyuan Guo,  Shaofu Yang and  Jun Wang, "Global Synchronization of Stochastically Disturbed Memristive Neurodynamics via Discontinuous Control Laws," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 2, pp. 121-131, 2016.
Citation: Zhenyuan Guo,  Shaofu Yang and  Jun Wang, "Global Synchronization of Stochastically Disturbed Memristive Neurodynamics via Discontinuous Control Laws," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 2, pp. 121-131, 2016.
shu

Global Synchronization of Stochastically Disturbed Memristive Neurodynamics via Discontinuous Control Laws

  • 1. College of Mathematics and Econometrics, Hunan University, Changsha, China;

  • 2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China;

  • 3. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China

Funds:

This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (416811,416812), National Natural Science Foundation of China (61573003), and in part by the Scientific Research Fund of Hunan Provincial Education Department of China (15k026).

    Abstract

  • This paper presents the theoretical results on the master-slave (or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First, a control law with a linear time-delay feedback term and a discontinuous feedback term is introduced. By utilizing the stability theory of stochastic differential equations, sufficient conditions are derived for ascertaining global synchronization in mean square using this control law. Second, an adaptive control law consisting of a linear feedback term and a discontinuous feedback term is designed to achieve global synchronization in mean square, and it does not need prior information of network parameters or random disturbances. Finally, simulation results are presented to substantiate the theoretical results.

     

    • FullText(HTML)
  • loading
    • References(64)
  • [1]
    Chua L O. Memristor-the missing circuit element. IEEE Transactions on Circuit Theory, 1971, 18(5): 507-519
    [2]
    Mathur N D. The fourth circuit element. Nature, 2008, 455(7217): E13
    [3]
    Strukov D B, Snider G S, Stewart D R, Williams R S. The missing memristor found. Nature, 2008, 453(7191): 80-83
    [4]
    Itoh M, Chua L O. Memristor cellular automata and memristor discretetime cellular neural networks. International Journal of Bifurcation and Chaos, 2009, 19(11): 3605-3656
    [5]
    Pershin Y V, Di Ventra M. Experimental demonstration of associative memory with memristive neural networks. Neural Networks, 2010, 23(7): 881-886
    [6]
    Cao J D, Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003, 50(1): 34-44
    [7]
    Cao J D, Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Transactions on Circuits and Systems I: Regular Papers, 2005, 52(2): 417-426
    [8]
    Wang Z S, Zhang H G, Jiang B. LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures. IEEE Transactions on Neural Networks, 2011, 22(7): 1032-1045
    [9]
    Zhang H G, Wang Z S, Liu D R. A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(7): 1229-1262
    [10]
    Wang Z S, Liu L, Shan Q H, Zhang H G. Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(10): 2589-2595 130 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 3, NO. 2, APRIL 2016
    [11]
    Wang Z, Ding S, Huang Z, Zhang H. Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Transactions on Neural Networks and Learning Systems, 2015, 1-14
    [12]
    Hu J, Wang J. Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In: Proceedings of the 2010 International Joint Conference on Neural Networks (IJCNN). Barcelona: IEEE, 2010. 1-8
    [13]
    Wu A L, Zeng Z G. Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays. Neural Networks, 2012, 36: 1-10
    [14]
    Wen S P, Zeng Z G, Huang T W. Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays. Neurocomputing, 2012, 97: 233-240
    [15]
    Guo Z Y, Wang J, Yan Z. Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Networks, 2013, 48: 158-172
    [16]
    Guo Z Y, Wang J, Yan Z. Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(4): 704-717
    [17]
    Guo Z Y, Wang J, Yan Z. Passivity and passification of memristor-based recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(11): 2099-2109
    [18]
    Pecora L M, Carroll T L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8): 821-824
    [19]
    Hansel D, Sompolinsky H. Synchronization and computation in a chaotic neural network. Physical Review Letters, 1992, 68(5): 718-721
    [20]
    Hoppensteadt F C, Izhikevich E M. Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Transactions on Neural Networks, 2000, 11(3): 734-738
    [21]
    Chen G R, Zhou J, Liu Z R. Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. International Journal of Bifurcation and Chaos, 2004, 14(7): 2229-2240
    [22]
    Lu W, Chen T. Synchronization of coupled connected neural networks with delays. IEEE Transactions on Circuits and Systems I: Regular Papers, 2004, 51(12): 2491-2503
    [23]
    Wu W, Chen T P. Global synchronization criteria of linearly coupled neural network systems with time-varying coupling. IEEE Transactions on Neural Networks, 2008, 19(2): 319-332
    [24]
    Liang J L, Wang Z D, Liu Y R, Liu X H. Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2008, 38(4): 1073-1083
    [25]
    Yu W W, Chen G R, Lu J H. On pinning synchronization of complex dynamical networks. Automatica, 2009, 45(2): 429-435
    [26]
    Lu J Q, Ho D W C, Cao J D. A unified synchronization criterion for impulsive dynamical networks. Automatica, 2010, 46(7): 1215-1221
    [27]
    Liu T, Zhao J, Hill D J. Exponential synchronization of complex delayed dynamical networks with switching topology. IEEE Transactions on Circuits and Systems I: Regular Papers, 2010, 57(11): 2967-2980
    [28]
    Zhang W B, Tang Y, Miao Q Y, Du W. Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(8): 1316-1326
    [29]
    Wu L G, Feng Z G, Lam J. Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(12): 1957-1972
    [30]
    Tang Y, Wai K W. Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(3): 435-447
    [31]
    Liu Y R, Wang Z D, Liang J L, Liu X H. Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays. IEEE Transactions on Cybernetics, 2013, 43(1): 102-114
    [32]
    Cao J D, Chen G R, Li P. Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2008, 38(2): 488-498
    [33]
    Lu H T, van Leeuwen C. Synchronization of chaotic neural networks via output or state coupling. Chaos, Solitons & Fractals, 2006, 30(1): 166-176
    [34]
    Cao J D, Lu J Q. Adaptive synchronization of neural networks with or without time-varying delay. Chaos, 2006, 16(1): 013133
    [35]
    Wu Z G, Shi P, Su H Y, Chu J. Sampled-data synchronization of chaotic Lur'e systems with time delays. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(3): 410-421
    [36]
    Zhang H G, Ma T D, Huang G B, Wang Z X. Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40(3): 831-844
    [37]
    Wu A L, Wen S P, Zeng Z G. Synchronization control of a class of memristor-based recurrent neural networks. Information Sciences, 2012, 183(1): 106-116
    [38]
    Zhang G D, Shen Y. New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(10): 1701-1707
    [39]
    Wen S P, Bao G, Zeng Z G, Chen Y R, Huang T W. Global exponential synchronization of memristor-based recurrent neural networks with timevarying delays. Neural Networks, 2013, 48: 195-203
    [40]
    Zhang G D, Shen Y. Exponential synchronization of delayed memristorbased chaotic neural networks via periodically intermittent control. Neural Networks, 2014, 55: 1-10
    [41]
    Yang X S, Cao J D, Yu W W. Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays. Cognitive Neurodynamics, 2014, 8(3): 239-249
    [42]
    Chen J J, Zeng Z G, Jiang P. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Networks, 2014, 51: 1-8
    [43]
    Guo Z Y, Wang J, Yan Z. Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015, 45(2): 235-249
    [44]
    Guo Z Y, Yang S F, Wang J. Global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(6): 1300-131132
    [45]
    Yang S F, Guo Z Y, Wang J. Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015, 45(7): 1077-1086
    [46]
    Tuckwell H C. Stochastic Processes in the Neurosciences. Philadelphia, PA: SIAM, 1989.
    [47]
    Haykin S. Kalman Filtering and Neural Networks. New York: Wiley, 2001.
    [48]
    Huang H, Ho D W C, Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Transactions on Circuits and Systems II: Express Briefs, 2005, 52(5): 251-255
    [49]
    Wang Z D, Liu Y R, Li M Z, Liu X H. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks, 2006, 17(3): 814-820
    [50]
    Liang J L, Wang Z D, Liu Y R, Liu X H. Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Transactions on Neural Networks, 2008, 19(11): 1910-1921
    [51]
    Wang Z D, Wang Y, Liu Y R. Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Transactions on Neural Networks, 2010, 21(1): 11-25
    [52]
    Huang C X, Cao J D. Convergence dynamics of stochastic Cohen- Grossberg neural networks with unbounded distributed delays. IEEE Transactions on Neural Networks, 2011, 22(4): 561-572
    [53]
    Lu J Q, Kurths J, Cao J D, Mahdavi N, Huang C. Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(2): 285-292
    [54]
    Zhang W B, Tang Y, Miao Q Y, Fang J A. Synchronization of stochastic dynamical networks under impulsive control with time delays. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(10): 1758-1768
    [55]
    Yang X S, Cao J D, Qiu J L. pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Networks, 2015, 65: 80-91
    [56]
    Ding S B, Wang Z S. Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing, 2015, 162: 16-25
    [57]
    Øksendal B. Stochastic Differential Equations. Berlin Heidelberg: Springer, 2003.
    [58]
    Chua L. Resistance switching memories are memristors. Applied Physics A, 2011, 102(4): 765-783
    [59]
    Jo S H, Chang T, Ebong I, Bhadviya B B, Mazumder P, Lu W. Nanoscale memristor device as synapse in neuromorphic systems. Nano Letters, 2010, 10(4): 1297-1301
    [60]
    Sah M P, Yang C J, Kim H, Chua L. A voltage mode memristor bridge synaptic circuit with memristor emulators. Sensors, 2012, 12(3): 3587-3604
    [61]
    Kim H, Sah M P, Yang C J, Roska T, Chua L O. Neural synaptic weighting with a pulse-based memristor circuit. IEEE Transactions on Circuits and Systems I: Regular Papers, 2012, 59(1): 148-158
    [62]
    Adhikari S P, Yang C J, Kim H, Chua L O. Memristor bridge synapsebased neural network and its learning. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(9): 1426-1435
    [63]
    Boyd S, El Ghaoui L, Feron E, Balakrishnan B. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
    [64]
    Edwards C, Spurgeon S K, Patton R J. Sliding mode observers for fault detection and isolation. Automatica, 2000, 36(4): 541-553
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1124) PDF downloads(12) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return