搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于状态观测器的分数阶时滞混沌系统同步研究

贾雅琼 蒋国平

引用本文:
Citation:

基于状态观测器的分数阶时滞混沌系统同步研究

贾雅琼, 蒋国平

Chaotic system synchronization of state-observer-based fractional-order time-delay

Jia Ya-Qiong, Jiang Guo-Ping
PDF
导出引用
  • 研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.
    A lot of studies of control highlight fractional calculus in modeling systems and designing controllers have been carried out. More recently, a lot of chaotic behaviors have been found in fractional-order systems. Then, controlling the fractional-order systems, especially controlling nonlinear fractional-order systems has become a hot research subject. The design of state estimators is one of the essential points in control theory. Time delays are often considered as the sources of complex behaviors in dynamical systems. A lot progress has been made in the research of time delay systems with real variables. In recent years, fractional-order time-delay chaotic synchronization and chaotic secure communication have received ever-increasing attention. In this paper we focus our study on the synchronization of fractional-order time-delay chaotic systems and its application in secure communication. Firstly, based on the Lipschitz condition, the nonlinear fractional-order time-delay system is proposed. Secondly, the fractional-order time-delay observer for the system is constructed. The necessary and sufficient conditions for the existence of the fractional-order observer are given by some lemmas. Thirdly, the synchronous controller is designed based on the state observer and the stability theory of fractional-order system. Instead of the state variables, the output variables of drive system and response system are used to design the synchronous controller, which makes the design much more simple and practical. With the Lyapunov stability theory and fractional order matrix inequalities, the method of how to obtain the parameters of the controller is presented. The sufficient conditions for asymptotical stability of the state error dynamical system are derived. After that, with the Chen fractional-order time-delay chaotic system, the synchronous controller is designed to make the system run synchronously. Finally, the proposed approach is then applied to secure communications, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. With the observer design technique, a chaotic receiver is then derived to recover the information signal at the receiving end of the communication. In the conventional chaotic masking method, the receiver is driven by the sum of the information signal and the output of the transmitter, whose dynamics is autonomous. The simulation results show that the design of the synchronous controller works effectively and efficiently, which implies that the proposed fractional order time-delay observer in this paper runs effectively. The proposed method is able to be applied to other fractional order time-delay chaos systems, and also to chaotic secure communication system.
      通信作者: 蒋国平, jianggp@njupt.edu.cn
    • 基金项目: 国家自然科学基金(批准号:61374180,61373136,61401226,61672298)、湖南省教育厅项目(批准号:15C0369)和湖南工学院重点学科建设资助项目资助的课题.
      Corresponding author: Jiang Guo-Ping, jianggp@njupt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61374180, 61373136, 61401226, 61672298), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 15C0369), and the Program of the Key Disciplinary in Hunan Institute of Technology.
    [1]

    Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524 (in Chinese)[许喆, 刘崇新, 杨韬2010物理学报59 1524]

    [2]

    Ardashir M, Sehraneh G, Okyay K, Sohrab K 2016 Appl. Soft. Comput. 49 544

    [3]

    Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese)[梁义, 王兴元2013物理学报62 018901]

    [4]

    Ou Y C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese)[欧阳成, 林万涛, 程荣军, 莫嘉琪2013物理学报62 060201]

    [5]

    Faieghi M R, Delavari H 2012 Commu. Non. Sci. Num. Simu. 17731

    [6]

    Xu J, Pei L J 2006 Adv. Mech. 36 17 (in Chinese)[徐鉴, 裴利军2006力学进展36 17]

    [7]

    Cai Q Q 2015 Acta Phys. Sin. 64 240506 (in Chinese)[柴琴琴2015物理学报64 240506]

    [8]

    Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese)[黄丽莲, 马楠2012物理学报61 160510]

    [9]

    Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese)[牛弘, 张国山2013物理学报62 130502]

    [10]

    Gamal M M, Emad E M, Ayman A A 2015 Nonlin. Dyn. 80 855

    [11]

    Velmurugan G, Rakkiyappan R 2016 J. Comput. Nonlin. Dyn. 11 031016

    [12]

    Song Z 2016 Complexity 21 131

    [13]

    Song X N, Song S A, Li B 2016 Optik 127 11860

    [14]

    Jiang G P, Zheng W X, Tang W K, Chen G R 2006 IEEE Trans. Circuits-Ⅱ 53 110

    [15]

    Jiang G P, Chen G R, Tang W K 2004 IEEE Trans. Circuits-Ⅱ 51 281

    [16]

    He S B, Sun K H, Wang H H 2014 Acta Phys. Sin. 63 030502(in Chinese)[贺少波, 孙克辉, 王会海2013物理学报62 030502]

    [17]

    Deng W 2014 Adv. Comput. Math. 40 174

    [18]

    Petráš I 2010 Commu. Non. Sci. Num. Simu. 15 384

    [19]

    Ibrahima N D, Holger V, Mohamed D 2013 IEEE J. Emer. Sele. Top. Circ. Syst. 3 442

    [20]

    Li Y, Chen Y, Podlubny I 2010 Comput. Math. Appl. 59 1810

    [21]

    Mahdi P, Elham A B 2016 Circ. Syst. Signal Pr. 35 1855

    [22]

    Darouach M, Zasadzinski M, Xu S 1994 IEEE Trans. Automat. Contr. 39 606

  • [1]

    Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524 (in Chinese)[许喆, 刘崇新, 杨韬2010物理学报59 1524]

    [2]

    Ardashir M, Sehraneh G, Okyay K, Sohrab K 2016 Appl. Soft. Comput. 49 544

    [3]

    Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese)[梁义, 王兴元2013物理学报62 018901]

    [4]

    Ou Y C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese)[欧阳成, 林万涛, 程荣军, 莫嘉琪2013物理学报62 060201]

    [5]

    Faieghi M R, Delavari H 2012 Commu. Non. Sci. Num. Simu. 17731

    [6]

    Xu J, Pei L J 2006 Adv. Mech. 36 17 (in Chinese)[徐鉴, 裴利军2006力学进展36 17]

    [7]

    Cai Q Q 2015 Acta Phys. Sin. 64 240506 (in Chinese)[柴琴琴2015物理学报64 240506]

    [8]

    Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese)[黄丽莲, 马楠2012物理学报61 160510]

    [9]

    Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese)[牛弘, 张国山2013物理学报62 130502]

    [10]

    Gamal M M, Emad E M, Ayman A A 2015 Nonlin. Dyn. 80 855

    [11]

    Velmurugan G, Rakkiyappan R 2016 J. Comput. Nonlin. Dyn. 11 031016

    [12]

    Song Z 2016 Complexity 21 131

    [13]

    Song X N, Song S A, Li B 2016 Optik 127 11860

    [14]

    Jiang G P, Zheng W X, Tang W K, Chen G R 2006 IEEE Trans. Circuits-Ⅱ 53 110

    [15]

    Jiang G P, Chen G R, Tang W K 2004 IEEE Trans. Circuits-Ⅱ 51 281

    [16]

    He S B, Sun K H, Wang H H 2014 Acta Phys. Sin. 63 030502(in Chinese)[贺少波, 孙克辉, 王会海2013物理学报62 030502]

    [17]

    Deng W 2014 Adv. Comput. Math. 40 174

    [18]

    Petráš I 2010 Commu. Non. Sci. Num. Simu. 15 384

    [19]

    Ibrahima N D, Holger V, Mohamed D 2013 IEEE J. Emer. Sele. Top. Circ. Syst. 3 442

    [20]

    Li Y, Chen Y, Podlubny I 2010 Comput. Math. Appl. 59 1810

    [21]

    Mahdi P, Elham A B 2016 Circ. Syst. Signal Pr. 35 1855

    [22]

    Darouach M, Zasadzinski M, Xu S 1994 IEEE Trans. Automat. Contr. 39 606

  • [1] 林飞飞, 曾喆昭. 不确定分数阶时滞混沌系统自适应神经网络同步控制. 物理学报, 2017, 66(9): 090504. doi: 10.7498/aps.66.090504
    [2] 潘光, 魏静. 一种分数阶混沌系统同步的自适应滑模控制器设计. 物理学报, 2015, 64(4): 040505. doi: 10.7498/aps.64.040505
    [3] 王斌, 薛建议, 贺好艳, 朱德兰. 基于线性矩阵不等式的一类新羽翼倍增混沌分析与控制. 物理学报, 2014, 63(21): 210502. doi: 10.7498/aps.63.210502
    [4] 黄丽莲, 齐雪. 基于自适应滑模控制的不同维分数阶混沌系统的同步. 物理学报, 2013, 62(8): 080507. doi: 10.7498/aps.62.080507
    [5] 马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正. 一类分数阶混沌系统的自适应同步. 物理学报, 2012, 61(16): 160506. doi: 10.7498/aps.61.160506
    [6] 马铁东, 江伟波, 浮洁. 基于比较系统方法的分数阶混沌系统脉冲同步控制. 物理学报, 2012, 61(9): 090503. doi: 10.7498/aps.61.090503
    [7] 孙宁. 基于区间系统理论的分数阶混沌系统同步. 物理学报, 2011, 60(12): 120506. doi: 10.7498/aps.60.120506
    [8] 周平, 邝菲. 分数阶混沌系统与整数阶混沌系统之间的同步. 物理学报, 2010, 59(10): 6851-6858. doi: 10.7498/aps.59.6851
    [9] 张若洵, 杨世平, 刘永利. 基于线性控制的分数阶统一混沌系统的同步. 物理学报, 2010, 59(3): 1549-1553. doi: 10.7498/aps.59.1549
    [10] 付士慧, 裴利军. 具有非线性控制的Chua电路的混沌同步. 物理学报, 2010, 59(9): 5985-5989. doi: 10.7498/aps.59.5985
    [11] 杨东升, 张化光, 赵琰, 宋崇辉, 王迎春. 基于LMI的参数未知时变时滞混沌系统模糊自适应H∞同步. 物理学报, 2010, 59(3): 1562-1567. doi: 10.7498/aps.59.1562
    [12] 张若洵, 杨世平. 一个分数阶新超混沌系统的同步. 物理学报, 2008, 57(11): 6837-6843. doi: 10.7498/aps.57.6837
    [13] 李秀春, 徐 伟, 肖玉柱. 基于积分观测器实现一类受扰混沌系统的同步. 物理学报, 2008, 57(3): 1465-1470. doi: 10.7498/aps.57.1465
    [14] 朱志宇. 基于反馈精确线性化的混沌系统同步控制方法. 物理学报, 2006, 55(12): 6248-6252. doi: 10.7498/aps.55.6248
    [15] 王发强, 刘崇新. Liu混沌系统的线性反馈同步控制及电路实验的研究. 物理学报, 2006, 55(10): 5055-5060. doi: 10.7498/aps.55.5055
    [16] 王兴元, 刘 明. 用滑模控制方法实现具有扇区非线性输入的主从混沌系统同步. 物理学报, 2005, 54(6): 2584-2589. doi: 10.7498/aps.54.2584
    [17] 陈志盛, 孙克辉, 张泰山. Liu混沌系统的非线性反馈同步控制. 物理学报, 2005, 54(6): 2580-2583. doi: 10.7498/aps.54.2580
    [18] 窦春霞, 张淑清. 基于观测器的模型不确定的耦合时空混沌H∞跟踪控制. 物理学报, 2004, 53(12): 4120-4125. doi: 10.7498/aps.53.4120
    [19] 吴忠强, 岳东, 许世范. Chua混沌系统的一种模糊控制器设计——LMI法. 物理学报, 2002, 51(6): 1193-1197. doi: 10.7498/aps.51.1193
    [20] 刘福才, 王娟, 石淼, 高秀伟. 混沌系统的非线性连续预测变结构控制与同步. 物理学报, 2002, 51(12): 2707-2712. doi: 10.7498/aps.51.2707
计量
  • 文章访问数:  3609
  • PDF下载量:  348
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-02-17
  • 修回日期:  2017-06-12
  • 刊出日期:  2017-08-05

基于状态观测器的分数阶时滞混沌系统同步研究

  • 1. 南京邮电大学自动化学院, 南京 210023;
  • 2. 湖南工学院电气与信息工程学院, 信号与信息处理重点实验室, 衡阳 421002
  • 通信作者: 蒋国平, jianggp@njupt.edu.cn
    基金项目: 国家自然科学基金(批准号:61374180,61373136,61401226,61672298)、湖南省教育厅项目(批准号:15C0369)和湖南工学院重点学科建设资助项目资助的课题.

摘要: 研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性.

English Abstract

参考文献 (22)

目录

    /

    返回文章
    返回