中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3742-3750.doi: 10.1088/1674-1056/18/9/022

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Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

佟绍成1, 张化光2, 马铁东3, 浮洁3   

  1. (1)Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou 121001, China; (2)Key Laboratory of Integrated Automation for the Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China;School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; (3)School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
  • 收稿日期:2008-12-03 修回日期:2009-02-15 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60534010, 60774048, 60728307, 60804006 and 60521003), the National High Technology Research and Development Program of China (Grant No 2006AA04Z183), Liaoning Provincial Natural Science Foundation, China (Grant No 20062018), the State Key Development Program for Basic Research of China (Grant No 2009CB320601) and 111 Project (Grant No B08015).

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

Zhang Hua-Guang(张化光)a)b)†, Ma Tie-Dong(马铁东)b), Fu Jie(浮洁)b), and Tong Shao-Cheng(佟绍成)c)   

  1. a Key Laboratory of Integrated Automation for the Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China; b School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; c Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou 121001, China
  • Received:2008-12-03 Revised:2009-02-15 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60534010, 60774048, 60728307, 60804006 and 60521003), the National High Technology Research and Development Program of China (Grant No 2006AA04Z183), Liaoning Provincial Natural Science Foundation, China (Grant No 20062018), the State Key Development Program for Basic Research of China (Grant No 2009CB320601) and 111 Project (Grant No B08015).

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摘要： In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.

Abstract: In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.

Key words: exponential synchronization, chaotic delayed neural networks, impulsive control, stochastic perturbation

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.30.Yy (Control theory) 02.50.Ey (Stochastic processes) 05.45.Gg (Control of chaos, applications of chaos) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)