基于Min-Max方法的混沌系统采样同步控制研究

任涛; 朱志良; 于海; 王猛

doi:10.7498/aps.62.170510

摘要

针对含有扰动的混沌系统, 设计采样同步控制器, 利用输入时滞法将含有采样同步控制器的混杂系统转换为具有输入时滞的连续系统. 并考虑对系统影响最坏的干扰程度, 在该种情况下, 基于线性矩阵不等式(LMI)技术和min-max鲁棒控制方法, 给出了使误差系统稳定的充分条件, 确保混沌系统在所容许的扰动下均能实现完全同步. 仿真结果说明所设计的采样同步控制方案具有很强的鲁棒性, 适合应用于保密通信系统中.

关键词:

Abstract

For the chaotic systems with disturbance, a sampled-data controller is designed to achieve chaotic synchronization. Firstly, to handle the discontinuity introduced by the sampling activities, the input-delay approach is introduced to transform the discontinuous chaotic systems into continuous ones. Secondly, the worst possible case of performance is considered according to min-max robust strategy. Then the sufficient conditions for global asymptotic synchronization of such chaotic systems are derived and expressed in terms of linear matrix inequality (LMI). The proposed algorithm can achieve synchronization of the sampled-data chaotic systems for all admissible disturbances at the pre-computed set of disturbance realizations. The effectiveness is finally illustrated via numerical simulations of chaotic Chuas circuit, and the simulation results show that the proposed algorithm is suitable for secure communication.

Keywords:

作者及机构信息

1.
东北大学, 软件学院, 沈阳 110011;

2.
东北大学, 信息科学与工程学院, 沈阳 110011

基金项目: 国家自然科学基金青年科学基金(批准号: 61104074)、中国博士后科学基金(批准号: 20100471462, 2013T60294);中央高校基本科研业务费专项资金(批准号: N100317002, N100604007, N110417004, N110417005, N110617001)和辽宁省博士启动基金(批准号: 20101032)资助的课题.

Authors and contacts

1.
Software College, Northeastern University, Shenyang 110011, China;

2.
School of Information Science and Engineering, Northeastern University, Shenyang 110011, China

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61104074), the China Postdoctoral Science Foundation (Grant Nos. 20100471462, 2013T60294), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. N100317002, N100604007, N110417004, N110417005, N110617001), and the Scientific Research Foundation for Doctor of Liaoning Province, China (Grant No. 20101032).

参考文献

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[2]	Ji Y, Wen C Y, Li Z G 2008 Int. J. Comm. Sys. 21 1137
[3]	Li J F, Li N 2002 Chin. Phys. 11 1124
[4]	Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[5]	Wang X Y, Wu X J, He Y J, Aniwar G 2008 Int. J. Modern Physics B 22 3709
[6]	Lee S M, Choi S J, Ji D H, Park J H, Won S C 2010 Nonlinear Dynam 59 277
[7]	Kwon O M, Park J H, Lee S M 2011 Nonlinear Dynam 63 239
[8]	Ma T D, Jiang W B, Fu J, Chai Y, Chen L P, Xue F Z 2012 Acta Phys. Sin. 61 160506 (in Chinese) [马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正 2012 61 160506]
[9]	Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 12508
[10]	Ma T D, Jiang W B, Fu J 2012 Acta Phys. Sin. 61 090503 (in Chinese) [马铁东, 江伟波, 浮洁 2012 61 090503]
[11]	Lee S H, Kapila V, Porfiri M, Panda A 2010 Commun. Nonlinear Sci. Numer. Simulat 15 4100
[12]	Lee S H, Kapila V, Porfiri M 2008 Proceedings of the American Control Conference Seattle, WA, USA, Jun 11-13, 2008 p523
[13]	Barajas-Ramirez J G, Chen G, Shieh L S 2003 Int. J. Bifurc. Chaos 13 1197
[14]	Barajas-Ramirez J G, Chen G, Shieh L S 2004 Int. J. Bifurc. Chaos 14 2721
[15]	Barajas-Ramirez J G, Chen G, Shieh L S 2003 Proceedings of IEEE International Symposium on Intelligent Control Houston Texas, USA, October 5-8, 2003 p241
[16]	Lam H K, Seneviratne L D 2008 IEEE Trans. Circuits Syst. I 55 883
[17]	Zhang C K, He Y, Wu M 2009 IEEE Trans. Circuits Syst. II 56 320
[18]	Lu J G, Hill D J 2008 IEEE Trans. Circuits Syst. II 55 586
[19]	Zhu X L, Wang Y Y, Yang H Y 2010 Proceedings of the American Control Conference Baltimore, MD, USA, June 30-July 02, 2010 p1817
[20]	Chen W H, Wang Z P, Lu X M 2012 IEEE Trans. Circuits Syst. II 59 515
[21]	Feng Y F, Zhang Q L 2011 Chin. Phys. B 20 1
[22]	Theesar S J S, Banerjee S, Balasubramaniam P 2012 Nonlinear Dynam 70 1977
[23]	Ma D Z, Zhang H G, Wang Z S, Feng J 2010 Chin. Phys. B 19 0505061
[24]	Lee T H, Park J H, Lee S M, Kwon O M 2013 Int. J. Control 86 107
[25]	Fridman E, Shaked U, Suplin V 2007 Automatica 43 1072
[26]	Fridman E, Shaked U, Suplin V 2007 Syst. Control Lett. 54 271

施引文献

[1]	Aziz-Alaoui M A 2005 Proceeding of the IEEE Conference on Electronics, Circuits and Systems Gammarth, Tunisia, December 11-14, 2005 p1
[2]	Ji Y, Wen C Y, Li Z G 2008 Int. J. Comm. Sys. 21 1137
[3]	Li J F, Li N 2002 Chin. Phys. 11 1124
[4]	Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[5]	Wang X Y, Wu X J, He Y J, Aniwar G 2008 Int. J. Modern Physics B 22 3709
[6]	Lee S M, Choi S J, Ji D H, Park J H, Won S C 2010 Nonlinear Dynam 59 277
[7]	Kwon O M, Park J H, Lee S M 2011 Nonlinear Dynam 63 239
[8]	Ma T D, Jiang W B, Fu J, Chai Y, Chen L P, Xue F Z 2012 Acta Phys. Sin. 61 160506 (in Chinese) [马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正 2012 61 160506]
[9]	Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 12508
[10]	Ma T D, Jiang W B, Fu J 2012 Acta Phys. Sin. 61 090503 (in Chinese) [马铁东, 江伟波, 浮洁 2012 61 090503]
[11]	Lee S H, Kapila V, Porfiri M, Panda A 2010 Commun. Nonlinear Sci. Numer. Simulat 15 4100
[12]	Lee S H, Kapila V, Porfiri M 2008 Proceedings of the American Control Conference Seattle, WA, USA, Jun 11-13, 2008 p523
[13]	Barajas-Ramirez J G, Chen G, Shieh L S 2003 Int. J. Bifurc. Chaos 13 1197
[14]	Barajas-Ramirez J G, Chen G, Shieh L S 2004 Int. J. Bifurc. Chaos 14 2721
[15]	Barajas-Ramirez J G, Chen G, Shieh L S 2003 Proceedings of IEEE International Symposium on Intelligent Control Houston Texas, USA, October 5-8, 2003 p241
[16]	Lam H K, Seneviratne L D 2008 IEEE Trans. Circuits Syst. I 55 883
[17]	Zhang C K, He Y, Wu M 2009 IEEE Trans. Circuits Syst. II 56 320
[18]	Lu J G, Hill D J 2008 IEEE Trans. Circuits Syst. II 55 586
[19]	Zhu X L, Wang Y Y, Yang H Y 2010 Proceedings of the American Control Conference Baltimore, MD, USA, June 30-July 02, 2010 p1817
[20]	Chen W H, Wang Z P, Lu X M 2012 IEEE Trans. Circuits Syst. II 59 515
[21]	Feng Y F, Zhang Q L 2011 Chin. Phys. B 20 1
[22]	Theesar S J S, Banerjee S, Balasubramaniam P 2012 Nonlinear Dynam 70 1977
[23]	Ma D Z, Zhang H G, Wang Z S, Feng J 2010 Chin. Phys. B 19 0505061
[24]	Lee T H, Park J H, Lee S M, Kwon O M 2013 Int. J. Control 86 107
[25]	Fridman E, Shaked U, Suplin V 2007 Automatica 43 1072
[26]	Fridman E, Shaked U, Suplin V 2007 Syst. Control Lett. 54 271

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