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基于激励滑模控制的分数阶神经网络的修正投影同步研究

张平奎 杨绪君

张平奎, 杨绪君. 基于激励滑模控制的分数阶神经网络的修正投影同步研究[J]. 应用数学和力学, 2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098
引用本文: 张平奎, 杨绪君. 基于激励滑模控制的分数阶神经网络的修正投影同步研究[J]. 应用数学和力学, 2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098
ZHANG Pingkui, YANG Xujun. Modified Projective Synchronization of a Class of Fractional-Order Neural Networks Based on Active Sliding Mode Control[J]. Applied Mathematics and Mechanics, 2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098
Citation: ZHANG Pingkui, YANG Xujun. Modified Projective Synchronization of a Class of Fractional-Order Neural Networks Based on Active Sliding Mode Control[J]. Applied Mathematics and Mechanics, 2018, 39(3): 343-354. doi: 10.21656/1000-0887.380098

基于激励滑模控制的分数阶神经网络的修正投影同步研究

doi: 10.21656/1000-0887.380098
基金项目: 国家自然科学基金(11501065)
详细信息
    作者简介:

    张平奎(1964—),男(E-mail: sxsfpxc@163.com);杨绪君(1989—),男,博士生(通讯作者. E-mail: ller2010@163.com).

  • 中图分类号: O175.13

Modified Projective Synchronization of a Class of Fractional-Order Neural Networks Based on Active Sliding Mode Control

Funds: The National Natural Science Foundation of China(11501065)
  • 摘要: 研究了分数阶神经网络的修正投影同步问题.首先通过选取合适的激励控制器来辅助设计滑模控制器.然后通过设计选取了合适的切换平面和有效的趋近率,并根据滑模控制理论和分数阶微分方程的基本理论,建立了使驱动系统和响应系统实现修正投影同步的激励滑模控制器.最后,通过数值仿真实例,验证了所得结果的有效性和可行性.
  • [1] PODLUBNY I. Fractional Differential Equations [M]. San Diego: Academic Press, 1999.
    [2] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and Applications of Fractional Differential Equations [M]. Amsterdam: Elsevier, 2006.
    [3] BOROOMAND A, MENHAJ M B. Fractional-order Hopfield neural networks[C]// International Conference on Neural Information Processing . Berlin, Heidelberg: Springer, 2008.
    [4] YANG Xujun, LI Chuandong, SONG Qiankun, et al. Mittag-Leffler stability analysis on variable-time impulsive fractional-order neural networks[J]. Neurocomputing,2016,207: 276-286.
    [5] KASLIK E, SIVASUNDARAM S. Nonlinear dynamics and chaos in fractional-order neural networks[J]. Neural Networks,2012,32: 245-256.
    [6] YANG Xujun, SONG Qiankun, LIU Yurong, et al. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing,2015,152: 19-26.
    [7] YU Juan, HU Cheng, JIANG Haijun. α-stability and α-synchronization for fractional-order neural networks[J]. Neural Networks, 2012,35: 82-87.
    [8] YANG Xujun, LI Chuandong, HUANG Tingwen, et al. Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses[J]. Applied Mathematics and Computation,2017,293: 416-422.
    [9] CHEN Jiejie, ZENG Zhigang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51: 1-8.
    [10] BAO Haibo, PARK J, CAO Jinde. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear Dynamics,2015,82: 1343-1354.
    [11] CHEN Liping, WU Ranchao, CAO Jinde, et al. Stability and synchronization of memristor-based fractional-order delayed neural networks[J]. Neural Networks,2015,71: 37-44.
    [12] BAO Haibo, CAO Jinde. Projective synchronization of fractional-order memristor-based neural networks[J]. Neural Networks,2015,63: 1-9.
    [13] 王利敏, 宋乾坤, 赵振江. 基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性[J]. 应用数学和力学, 2017,38(3): 333-346.(WANG Limin, SONG Qiankun, ZHAO Zhenjiang. Global asymptotic stability of memristor-based fractional-order complex-valued neural networks with time delays[J]. Applied Mathematics and Mechanics,2017,38(3): 333-346.(in Chinese))
    [14] YANG Xujun, LI Chuandong, HUANG Tingwen, et al. Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses[J]. Applied Mathematics and Computation,2017,293: 416-422.
    [15] YANG Xujun, LI Chuandong, HUANG Tingwen, et al. Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay[J]. Neurocomputing,2017,234: 205-215.
    [16] 陈志梅, 王贞艳, 张井刚. 滑模变结构控制理论及应用[M]. 北京: 电子工业出版社, 2012.(CHEN Zhimei, WANG Zhenyan, ZHANG Jinggang. Sliding Mode Variable Structure Control Theory and Application[M]. Beijing: Publishing House of Electronics Industry, 2012.(in Chinese))
    [17] TAVAZOEI M S, HAERI M. Synchronization of chaotic fractional-order systems via active sliding mode controller[J]. Physica A: Statistical Mechanics and Its Applications,2008,387(1): 57-70.
    [18] YANG Ningning, LIU Chongxin. A novel fractional-order hyperchaotic system stabilization via fractional sliding-mode control[J]. Nonlinear Dynamics,2013,74(3): 721-732.
    [19] YIN Chun, ZHONG Shouming, CHEN Wufan. Design of sliding mode controller for a class of fractional-order chaotic systems[J]. Communications in Nonlinear Science and Numerical Simulation,2012,17(1): 356-366.
    [20] CHEN Diyi, ZHANG Runfan, SPROTT J C, et al. Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control[J]. Chaos: an Interdisciplinary Journal of Nonlinear Science,2012,22(2): 023130.
    [21] DADRAS S, MOMENI H R. Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems[J].Mechatronics,2013,23(7): 880-887.
    [22] AGHABABA M P. Design of hierarchical terminal sliding mode control scheme for fractional-order systems[J]. IET Science, Measurement & Technology,2014,9(1): 122-133.
    [23] WANG Xingyuan, ZHANG Xiaopeng, MA Chao. Modified projective synchronization of fractional-order chaotic systems via active sliding mode control[J].Nonlinear Dynamics,2012,69(1/2): 511-517.
    [24] DING Zhixia, SHEN Yi. Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller[J].Neural Networks,2016,76: 97-105.
    [25] MATIGNON D. Stability results for fractional differential equations with applications to control processing[C]// Computational Engineering in Systems Applications.Lille, France, 1996,2: 963-968.
    [26] AGUILA-CAMACHO N, DUARTE-MERMOUD M A, GALLEGOS J A. Lyapunov functions for fractional order systems[J]. Communications in Nonlinear Science and Numerical Simulation,2014,19(9): 2951-2957.
    [27] DIETHELM K, FORD N J, FREED A D. A predictor-corrector approach for the numerical solution of fractional differential equations[J].Nonlinear Dynamics,2002,29(1/4): 3-22.
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出版历程
  • 收稿日期:  2017-04-13
  • 修回日期:  2017-06-28
  • 刊出日期:  2018-03-15

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