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

ZHANG Pingkui; YANG Xujun

doi:10.21656/1000-0887.380098

Volume 39 Issue 3

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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

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

doi: 10.21656/1000-0887.380098

ZHANG Pingkui¹,
YANG Xujun²

¹Institute of Continuing Education, Chongqing Preschool Education College, Chongqing 404047, P.R.China;²College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P.R.China

Funds: The National Natural Science Foundation of China(11501065)

Received Date: 2017-04-13
Rev Recd Date: 2017-06-28
Publish Date: 2018-03-15

Abstract

Abstract

The modified projective synchronization of a class of fractionalorder neural networks was studied. An appropriate active controller was firstly selected to facilitate the design of the sliding mode controller. Afterwards, a suitable switching plane and 2 effective reaching laws were defined and several criteria were established to ensure the synchronization of the driveresponse systems based on the sliding mode control theory and the theory of fractional differential equations. Numerical examples verify the validity and feasibility of the theoretical results.
- fractional-order neural network,
- modified projective synchronization,
- active control,
- sliding mode control

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References

[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.