基于滑模和反馈控制的鲁棒混沌系统同步

Li-li LI; Ying LIU; Qi-guo YAO

doi:10.1631/jzus.C1300266

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基于滑模和反馈控制的鲁棒混沌系统同步

计算机与自动化 | Updated：2022-05-19

- 基于滑模和反馈控制的鲁棒混沌系统同步
- Robust synchronization of chaotic systems using sliding mode and feedback control
- 信息与电子工程前沿（英文） 2014年15卷第3期页码：211-222
- Affiliations：
  
  1.School of Naval Architecture and Ocean Engineering, Zhejiang Ocean University, Zhoushan 316000, China
  2.Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  [ "Li-li LI, E-mail: 64452300@qq.com" ]
  Ying LIU, E-mail: yingliu@zju.edu.cn
  [ "Qi-guo YAO, E-mail: yaoqiguo@163.com" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 61101045), the Natural Science Foundation of Zhejiang Province of China (No. LY13E090004), and the Department of Graduate of Zhejiang Ocean University (No. 20(2012))
- DOI：10.1631/jzus.C1300266
  中图分类号： TP273
- 收稿：2013-09-21，
  
  修回：2014-2-19，
  
  录用：2013-12-13，
  
  纸质出版：2014-03
- Accepted：
Scan QR Code
基于滑模和反馈控制的鲁棒混沌系统同步[J]. 信息与电子工程前沿（英文）, 2014,15(3):211-222.

Li-li LI, Ying LIU, Qi-guo YAO. Robust synchronization of chaotic systems using sliding mode and feedback control[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(3): 211-222.
基于滑模和反馈控制的鲁棒混沌系统同步[J]. 信息与电子工程前沿（英文）, 2014,15(3):211-222. DOI： 10.1631/jzus.C1300266.

Li-li LI, Ying LIU, Qi-guo YAO. Robust synchronization of chaotic systems using sliding mode and feedback control[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(3): 211-222. DOI： 10.1631/jzus.C1300266.

摘要

研究目的

混沌同步是近年非线性系统研究热点，在许多方面具有重要应用。实际系统往往存在一定的不确定性，如系统模型以及系统参数的不匹配性等，严重影响了同步性能。本文提出一种鲁棒混沌同步方法，以实现带有一定不确定性的混沌系统的同步。

创新要点

将高阶滑模控制和反馈控制有效结合，设计了一种鲁棒的混沌同步控制策略。

方法提亮

该方法综合了滑模控制和反馈控制两方面优势，具有鲁棒性强、抗系统模型以及参数不匹配性好、收敛速度快、同步误差小的特点，因而特别适用于实际工程系统。

重要结论

理论分析证明了该方法的稳定性。通过和已有方法比较，数值仿真实验进一步验证了该方法的有效性。

Abstract

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives

while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically

and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms

the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.

关键词

Keywords

references

G. Besancon . Remarks on nonlinear adaptive observer design . Syst. Contr. Lett. , 2000 . 41 ( 4 ): 271 - 280 . DOI: 10.1016/S0167-6911(00)00065-7 http://doi.org/10.1016/S0167-6911(00)00065-7 .

S. Bowong . Stability analysis for the synchronization of chaotic systems with different order: application to secure communications . Phys. Lett. A , 2004 . 326 ( 1-2 ): 102 - 113 . DOI: 10.1016/j.physleta.2004.04.004 http://doi.org/10.1016/j.physleta.2004.04.004 .

M. Chen , J. Kurths . Chaos synchronization and parameter estimation from a scalar output signal . Phys. Rev. E , 2007 . 76 ( 2 ): 027203 DOI: 10.1103/PhysRevE.76.027203 http://doi.org/10.1103/PhysRevE.76.027203 .

J.J. Collins , I.N. Stewart . Coupled nonlinear oscillators and the symmetries of animal gaits . J. Nonl. Sci. , 1993 . 3 ( 1 ): 349 - 392 . DOI: 10.1007/BF02429870 http://doi.org/10.1007/BF02429870 .

M. Feki . An adaptive chaos synchronization scheme applied to secure communication . Chaos Sol. Fract. , 2003 . 18 ( 1 ): 141 - 148 . DOI: 10.1016/S0960-0779(02)00585-4 http://doi.org/10.1016/S0960-0779(02)00585-4 .

R. Femat , G. Solis-Perales . Robust Synchronization of Chaotic Systems via Feedback . Springer , 2008 . DOI: 10.1007/978-3-540-69307-9 http://doi.org/10.1007/978-3-540-69307-9 .

R. Femat , J. Alvarez-Ramírez , B. Castillo-Toledo , 等 . On robust chaos suppression in a class of nonlinear oscillators: application to Chua's circuit . IEEE Trans. Circ. Syst. Ⅰ , 1999 . 46 ( 9 ): 1150 - 1152 . DOI: 10.1109/81.788818 http://doi.org/10.1109/81.788818 .

R. Femat , J. Alvarez-Ramírez , G. Fernández-Anaya . Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization . Phys. D , 2000 . 139 ( 3-4 ): 231 - 246 . DOI: 10.1016/S0167-2789(99)00226-2 http://doi.org/10.1016/S0167-2789(99)00226-2 .

R. Femat , R.J. Ortiz , G.S. Perales . An adaptive chaos synchronization scheme applied to secure communication scheme via robust asymptotic feedback . IEEE Trans. Circ. Syst. Ⅰ , 2001 . 48 ( 10 ): 1161 - 1169 . .

U.S. Freitas , E.E.N. Macau , C. Grebogi . Using geometric control and chaotic synchronization to estimate an unknown model parameter . Phys. Rev. E , 2005 . 71 ( 4 ): 047203 DOI: 10.1103/PhysRevE.71.047203 http://doi.org/10.1103/PhysRevE.71.047203 .

G. Grassi , S. Mascoio . Synchronizing hyperchaotic systems by observer design . IEEE Trans. Circ. Syst. Ⅱ , 1999 . 46 ( 4 ): 478 - 483 . DOI: 10.1109/82.755422 http://doi.org/10.1109/82.755422 .

J.W. Haefner . Modeling Biological Systems: Principles and Applications , : New York, USA Springer , 2005 .

J.Q. Han . The extended state observer of a class of uncertain systems . Contr. & Dec. , 1995 . 110 ( 1 ): 85 - 88 . .

A Isidori . Nonlinear Control System , : Berlin, Germany Springer-Verlag , 1989 .

H.R. Karimi . Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations . Int. J. Contr. Automat. Syst. , 2011 . 9 ( 4 ): 671 - 680 . DOI: 10.1007/s12555-011-0408-8 http://doi.org/10.1007/s12555-011-0408-8 .

H.R. Karimi . A sliding mode approach to H ∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties . J. Franklin Inst. , 2012 . 349 ( 4 ): 1480 - 1496 . DOI: 10.1016/j.jfranklin.2011.09.015 http://doi.org/10.1016/j.jfranklin.2011.09.015 .

H.R. Karimi , H. Gao . New delay-dependent exponential H ∞ synchronization for uncertain neural networks with mixed time-delays . IEEE Trans. Syst. Man Cybern. Part B , 2010 . 40 ( 1 ): 173 - 185 . DOI: 10.1109/TSMCB.2009.2024408 http://doi.org/10.1109/TSMCB.2009.2024408 .

L. Kocarev , U. Parlitz . General approach for chaotic synchronization with applications to communication . Phys. Rev. Lett. , 1995 . 74 ( 25 ): 5028 - 5031 . DOI: 10.1103/PhysRevLett.74.5028 http://doi.org/10.1103/PhysRevLett.74.5028 .

A. Levant . Higher-order sliding modes, differentiation and output-feedback control . Int. J. Contr. , 2003 . 76 ( 9-10 ): 924 - 941 . DOI: 10.1080/0020717031000099029 http://doi.org/10.1080/0020717031000099029 .

A. Levant , Y. Pavlov . Generalized homogeneous quasi-continuous controllers . Int. J. Robust Nonl. Contr. , 2008 . 18 ( 4-5 ): 385 - 398 . DOI: 10.1002/rnc.1199 http://doi.org/10.1002/rnc.1199 .

X.R. Li , L.Y. Zhao , G.Z. Zhao . Sliding mode control for synchronization of chaotic systems with structure or parameter mismatching . J. Zhejiang Univ.-Sci. , 2005 . 6 ( 6 ): 571 - 576 . DOI: 10.1631/jzus.2005.A0571 http://doi.org/10.1631/jzus.2005.A0571 .

Y. Liu , W. Tang . Adaptive synchronization of chaotic systems and its uses in cryptanalysis. In : Recent Advances in Nonlinear Dynamics and Synchronization (NDS-1), Theory and Applications . Springer , 2009 . 254 307 - 346 . .

Y. Liu , W. Tang , L. Kocarev . An adaptive observer design for the auto-synchronization of Lorenz system . Int. J. Bifurcat. Chaos , 2008 . 18 ( 8 ): 2415 - 2423 . DOI: 10.1142/S0218127408021786 http://doi.org/10.1142/S0218127408021786 .

Y. Mao . Adaptive Synchronization and Its Use in Biological Neural Network Modeling . MS Thesis, City University of Hong Kong, Hong Kong, China , 2009 .

Y. Mao , W. Tang , Y. Liu , 等 . Identification of biological neurons using adaptive observers . Cogn. Process. , 2009 . 10 ( Suppl 1 ): 41 - 53 . DOI: 10.1007/s10339-008-0230-2 http://doi.org/10.1007/s10339-008-0230-2 .

H. Nijmeijer , I.M.Y. Mareels . An observer looks at synchronization . IEEE Trans. Circ. Syst. I , 1997 . 44 ( 10 ): 882 - 890 . DOI: 10.1109/81.633877 http://doi.org/10.1109/81.633877 .

L.M. Pecora , T.L. Carroll . Synchronization in chaotic systems . Phys. Rev. Lett. , 1990 . 64 ( 8 ): 821 - 824 . .

L.M. Pecora , T.L. Carroll . Driving systems with chaotic signals . Phys. Rev. A , 1991 . 44 ( 4 ): 2374 - 2383 . DOI: 10.1103/PhysRevA.44.2374 http://doi.org/10.1103/PhysRevA.44.2374 .

A. Rodríguez , J. de León , L. Fridman . Quasicontinuous high-order sliding-mode controllers for reduced-order chaos synchronization . Int. J. Nonl. Mech. , 2008 . 43 ( 9 ): 948 - 961 . DOI: 10.1016/j.ijnonlinmec.2008.07.007 http://doi.org/10.1016/j.ijnonlinmec.2008.07.007 .

H.L. Trentelman , K. Takaba , N. Monshizadeh . Robust synchronization of uncertain linear multi-agent systems . IEEE Trans. Automat. Contr. , 2013 . 58 ( 6 ): 1511 - 1523 . DOI: 10.1109/TAC.2013.2239011 http://doi.org/10.1109/TAC.2013.2239011 .

B. Wang , P. Shi , H.R. Karimi , 等 . H ∞ robust controller design for the synchronization of master-slave chaotic systems with disturbance input . Model. Identif. Contr. , 2012 . 33 ( 1 ): 27 - 34 . DOI: 10.4173/mic.2012.1.3 http://doi.org/10.4173/mic.2012.1.3 .

Y. Wang , D.T.M. Chik , Z.D. Wang . Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons . Phys. Rev. E , 2000 . 61 ( 1 ): 740 - 746 . DOI: 10.1103/PhysRevE.61.740 http://doi.org/10.1103/PhysRevE.61.740 .

S. Wittmeier , G. Song , J. Duffin , 等 . Pacemakers handshake synchronization mechanism of mammalian respiratory rhythmogenesis . PNAS , 2008 . 105 ( 46 ): 18000 - 18005 . DOI: 10.1073/pnas.0809377105 http://doi.org/10.1073/pnas.0809377105 .

J. Xu , L. Min , G. Chen . A chaotic communication scheme based on generalized synchronization and hash functions . Chin. Phys. Lett. , 2004 . 21 ( 8 ): 1445 - 1448 . DOI: 10.1088/0256-307X/21/8/009 http://doi.org/10.1088/0256-307X/21/8/009 .

T. Yang , H.H. Shao . Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design . Phys. Rev. E , 2002 . 65 ( 4 ): 046210 DOI: 10.1103/PhysRevE.65.046210 http://doi.org/10.1103/PhysRevE.65.046210 .

T. Youssef , M. Chadli , H.R. Karimi , 等 . Chaos synchronization based on unknown input proportional multiple-integral fuzzy observer . Abstr. Appl. Anal. , 2013 . 2013 670878 DOI: 10.1155/2013/670878 http://doi.org/10.1155/2013/670878 .

D. Yu , U. Parlitz . Estimating parameters by autosynchronization with dynamics restrictions . Phys. Rev. E , 2008 . 77 ( 6 Pt 2 ): 066221 DOI: 10.1103/PhysRevE.77.066221 http://doi.org/10.1103/PhysRevE.77.066221 .

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