基于比较系统方法的分数阶混沌系统脉冲同步控制

马铁东; 江伟波; 浮洁

doi:10.7498/aps.61.090503

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摘要

针对一类分数阶混沌系统的同步问题, 提出基于比较系统理论的脉冲同步方法. 通过构造新的响应系统, 可将原分数阶同步误差系统转化为整数阶同步误差系统, 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出一组新的分数阶混沌系统全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更为严格和实用. 通过对分数阶Chen系统同步问题的数值仿真研究, 验证了所提方法的有效性和可行性.

关键词:

作者及机构信息

1.
重庆大学自动化学院, 重庆 400044;

2.
重庆大学光电工程学院光电技术及系统教育部重点实验室, 重庆 400044

基金项目: 国家自然科学基金 (批准号: 61104080, 60804006), 重庆市自然科学基金 (批准号: CSTC,2010BB2238), 教育部博士点基金 (批准号: 20100191120025)和中国博士后科学基金 (批准号: 20100470813, 20100480043)资助的课题.

参考文献

[1]	Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[2]	Hartley T T, Lorenzo C F, Qammer H K 1995 IEEE Transactions CAS-I 42 485
[3]	Arena P, Caponetto R, Fortuna L, Porto D 1997 In: Proceedings ECCTD, Budapest 42 1259
[4]	Ahmad W M, Sprott J C 2003 Chaos Solitons and Fract. 16 339
[5]	Li C P, Peng G J 2004 Chaos Solitons and Fract. 22 443
[6]	Lu J G, Chen G R 2006 Chaos Solitons and Fract. 27 685
[7]	Lu J G 2006 Phys. Lett. A 354 305
[8]	Li C G, Chen G R 2004 Physica A 341 55
[9]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[10]	Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536
[11]	Taghvafard H, Erjaee G H 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4079
[12]	Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 物理学报 60 050510]
[13]	Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 物理学报 60 050511]
[14]	Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 物理学报 59 2305]
[15]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[16]	Wu C J, Zhang Y B, Yang N N 2011 Chin. Phys. B 20 060505
[17]	Wang X Y, Zhang Y L, Li D, Zhang N 2011 Chin. Phys. B 20 030506
[18]	Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33
[19]	Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B 40 831
[20]	Ma T D, Fu J, Sun Y 2010 Chin. Phys. B 19 090502
[21]	Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 物理学报 56 3796]
[22]	Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[23]	Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742
[24]	Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3751
[25]	Yang T 1999 IEEE Trans. Autom. Contr. 44 1081
[26]	Yang T 2001 Impulsive Control Theory (Berlin: Spinger-Verlag)
[27]	Podlubny I 1999 Fractional Differential Equations (New York: Academic)

施引文献

[1]	Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[2]	Hartley T T, Lorenzo C F, Qammer H K 1995 IEEE Transactions CAS-I 42 485
[3]	Arena P, Caponetto R, Fortuna L, Porto D 1997 In: Proceedings ECCTD, Budapest 42 1259
[4]	Ahmad W M, Sprott J C 2003 Chaos Solitons and Fract. 16 339
[5]	Li C P, Peng G J 2004 Chaos Solitons and Fract. 22 443
[6]	Lu J G, Chen G R 2006 Chaos Solitons and Fract. 27 685
[7]	Lu J G 2006 Phys. Lett. A 354 305
[8]	Li C G, Chen G R 2004 Physica A 341 55
[9]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[10]	Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536
[11]	Taghvafard H, Erjaee G H 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 4079
[12]	Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 物理学报 60 050510]
[13]	Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 物理学报 60 050511]
[14]	Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 物理学报 59 2305]
[15]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[16]	Wu C J, Zhang Y B, Yang N N 2011 Chin. Phys. B 20 060505
[17]	Wang X Y, Zhang Y L, Li D, Zhang N 2011 Chin. Phys. B 20 030506
[18]	Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33
[19]	Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B 40 831
[20]	Ma T D, Fu J, Sun Y 2010 Chin. Phys. B 19 090502
[21]	Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 物理学报 56 3796]
[22]	Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[23]	Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742
[24]	Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3751
[25]	Yang T 1999 IEEE Trans. Autom. Contr. 44 1081
[26]	Yang T 2001 Impulsive Control Theory (Berlin: Spinger-Verlag)
[27]	Podlubny I 1999 Fractional Differential Equations (New York: Academic)

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基于比较系统方法的分数阶混沌系统脉冲同步控制

1. 重庆大学自动化学院, 重庆 400044;

2. 重庆大学光电工程学院光电技术及系统教育部重点实验室, 重庆 400044

基金项目:

国家自然科学基金 (批准号: 61104080, 60804006), 重庆市自然科学基金 (批准号: CSTC,2010BB2238), 教育部博士点基金 (批准号: 20100191120025)和中国博士后科学基金 (批准号: 20100470813, 20100480043)资助的课题.

收稿日期: 2011-07-27

修回日期: 2012-05-10

刊出日期: 2012-05-05

摘要: 针对一类分数阶混沌系统的同步问题, 提出基于比较系统理论的脉冲同步方法. 通过构造新的响应系统, 可将原分数阶同步误差系统转化为整数阶同步误差系统, 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出一组新的分数阶混沌系统全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更为严格和实用. 通过对分数阶Chen系统同步问题的数值仿真研究, 验证了所提方法的有效性和可行性.

关键词:

Impulsive synchronization of fractional order hyperchaotic systems based on comparison system

1.
College of Automation, Chongqing University, Chongqing 400044, China;

2.
Key Lab of Optoelectronic Technology and System, Ministry of Education, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China

Fund Project:

Project supported by the National Natural Science Foundation of China (Grant Nos. 61104080, 60804006), the Natural Science Foundation of Chongqing (Grant No. CSTC, 2010BB2238), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100191120025), and the China postdoctoral science foundation (Grant Nos. 20100470813, 20100480043).

Received Date: 27 July 2011

Accepted Date: 10 May 2012

Published Online: 05 May 2012

Abstract: In this paper, a novel impulsive control method based on comparison system is proposed to realize complete synchronization of a class of fractional order chaotic systems. By constructing the suitable response system, the original fractional order error system can be converted into the integral order one. Based on the theory of Lyapunov stability and impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Compared with the existing results, the main results in this paper are more practical and rigorous. Simulation results for fractional order Chen system show the effectiveness and the feasibility of the proposed impulsive control method.

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