参数未知神经元模型的全阶与降阶最优同步

王兴元; 任小丽; 张永雷

doi:10.7498/aps.61.060508

摘要

基于Lyapunov稳定性理论、最优控制原理以及分步设计方法, 为神经元系统设计了非线性反馈控制器和最优控制器. 其中非线性反馈控制器能使得两个神经元系统之间的轨道误差趋于零, 最优控制器使得在同步过程中所花费的能量达到最低. 本文以Cable模型为例, 实现了两个神经元模型的全阶最优同步; 以Cable 模型和Hindmarsh-Rose (HR)模型为例, 实现了两个神经元模型的降阶最优同步; 同时, 均能有效地辨识出系统参数. 最后通过数值模拟进一步验证了本方案的有效性.

关键词:

Abstract

Based on Lyapunov stability theory, optimal control principle and step design methodology, nonlinear feedback controller and optimal controller are designed, in which the nonlinear feedback controller makes the trajectory error between two neuron systems tend to zero, and the optimal controller makes the spent energy meet minimum, which is spent in the process of synchronizing. In this paper, the uncertain cable model is taken as an example to illustrate the full-order optimal synchronization of two neurons. The uncertain cable model and the uncertain Hindmarsh-Rose (HR) model are taken to illustrate the reduced-order optimal synchronization of two neurons. In addition, the unknown parameters are identified successfully. Numerical Simulation results show the effectiveness of the strategy further.

Keywords:

作者及机构信息

1.
大连理工大学电子信息与电气工程学部, 大连 116024

通信作者: 王兴元, wangxy@dlut.edu.cn

基金项目: 国家自然科学基金(批准号:61173183,60573172,60973152)、高等学校博士学科点专项科研基金(批准号:20070141014)和辽宁省自然科学基金(批准号:20082165)资助的课题.

Authors and contacts

1.
School of Electronic & Information Engineering, Dalian University of Technology, Dalian 116024, China

Corresponding author: Wang Xing-Yuan, wangxy@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61173183, 60573172, 60973152), the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No. 20070141014), and the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165).

参考文献

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[3]	Hindmarsh J L, Rose R M 1984 P. Roy. Soc. Lond. B Biol. 221 87
[4]	Glass L 1995 Chaos in Neural Systems (Cambridge: MIT) p186
[5]	Roelfsema P R, Engel A K, K? nig P, Singer W 1997 Nature 385 157
[6]	Steriade M,McCormick D A, Sejnowski T J 1993 Science 262 679
[7]	Meister M, Wong R O, Baylor D A, Shatz C J 1991 Science 252 939
[8]	Kreiter A K, Singer W 1996 J. Neurosci. 16 2381
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[10]	Bennett M V L, Verselis V K 1992 Semin. Cell Biol. 3 29
[11]	Liu Y J,WangW, Tong S C, Liu Y S 2010 IEEE Trans. Syst. Man Cybern. Syst. Hum. 40 170
[12]	Liu Y J, Wen G X, Tong S C 2011 IEEE Trans. Neural Network 22 1162
[13]	Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[14]	Liu Y J, Zheng Y Q 2009 Nonlin. Dyn. 57 431
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[16]	Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[17]	Wang Q Y, Lu Q S, Chen G R, Guo D 2006 Phys. Lett. A 356 17
[18]	Cornejo-Pérez O, Femat R 2005 Chaos, Solitons and Fractals 25 43
[19]	Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE Trans. Neural Network. 18 1841
[20]	Song Y, Chen Z Q, Yuan Z Z 2007 Chin. J. Chem. Eng. 15 539
[21]	Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos, Solitons and Fractals 40 1333
[22]	Wang Q Y, Lua Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[23]	Awad E G 2006 Chaos, Solitons and Fractals 27 345
[24]	Terman D, Kopell N, Bose A 1998 Physica D 117 241
[25]	Schäfer C, Rosenblum M G, Abel H H, Kurths J R 1999 Phys. Rev. E 60 857
[26]	Bartsch R, Kantelhardt J W, Penzel T, Havlin S 2007 Phys. Rev. Lett. 98 054102 060508-6

施引文献

[1]	Chay T R 1985 Physica D 16 233
[2]	Thompson C J, Bardos D C, Yang Y S, Joyner K H 1999 Chaos, Solitons and Fractals 10 1825
[3]	Hindmarsh J L, Rose R M 1984 P. Roy. Soc. Lond. B Biol. 221 87
[4]	Glass L 1995 Chaos in Neural Systems (Cambridge: MIT) p186
[5]	Roelfsema P R, Engel A K, K? nig P, Singer W 1997 Nature 385 157
[6]	Steriade M,McCormick D A, Sejnowski T J 1993 Science 262 679
[7]	Meister M, Wong R O, Baylor D A, Shatz C J 1991 Science 252 939
[8]	Kreiter A K, Singer W 1996 J. Neurosci. 16 2381
[9]	Shuai J W, Durand D M 1999 Phys. Lett. A 264 289
[10]	Bennett M V L, Verselis V K 1992 Semin. Cell Biol. 3 29
[11]	Liu Y J,WangW, Tong S C, Liu Y S 2010 IEEE Trans. Syst. Man Cybern. Syst. Hum. 40 170
[12]	Liu Y J, Wen G X, Tong S C 2011 IEEE Trans. Neural Network 22 1162
[13]	Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[14]	Liu Y J, Zheng Y Q 2009 Nonlin. Dyn. 57 431
[15]	Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687 (in Chinese)[王占山, 张化光, 王智良 2006 物理学报 55 2687]
[16]	Dhamala M, Jirsa V K, Ding M 2004 Phys. Rev. Lett. 92 074104
[17]	Wang Q Y, Lu Q S, Chen G R, Guo D 2006 Phys. Lett. A 356 17
[18]	Cornejo-Pérez O, Femat R 2005 Chaos, Solitons and Fractals 25 43
[19]	Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE Trans. Neural Network. 18 1841
[20]	Song Y, Chen Z Q, Yuan Z Z 2007 Chin. J. Chem. Eng. 15 539
[21]	Che Y Q, Wang J, Zhou S S, Deng B 2009 Chaos, Solitons and Fractals 40 1333
[22]	Wang Q Y, Lua Q S, Chen G R, Guo D H 2006 Phys. Lett. A 356 17
[23]	Awad E G 2006 Chaos, Solitons and Fractals 27 345
[24]	Terman D, Kopell N, Bose A 1998 Physica D 117 241
[25]	Schäfer C, Rosenblum M G, Abel H H, Kurths J R 1999 Phys. Rev. E 60 857
[26]	Bartsch R, Kantelhardt J W, Penzel T, Havlin S 2007 Phys. Rev. Lett. 98 054102 060508-6

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