The study of finite-time stability active control method for Lorenz-Haken laser chaotic system

Zhao Jian-Li; Wang Jing; Wang Hui

doi:10.7498/aps.61.110209

Abstract

In this paper, the problem of finite-time stability for Lorenz-Haken laser chaotic system is studied by active control method. On the basis of the study for terminal attractor, and the consideration fo the uncertainties, an active control method with dynamic active compensation based on terminal attractor is proposed, which makes the controlled Lorenz-Haken laser chaotic system achieve the finite-time stability approximately. Meantime, in order to solve the uncertainties, a new observer is designed, which makes the estimate value follow the real value of uncertainties in a very short time. The approximate finite-time stability of the closed-loop system is analyzed in detail by introducing a singular perturbation theory. Simulation results show the effectiveness of the active control method and observer.

Keywords:

Authors and contacts

1.
National Engineer Research Center of Advanced Rolling, University of Science and Technology Beijing, Beijing 100083, China;
2.
Department of Information Security Engineering, Chinese People's Public Security University, Beijing 100038, China
Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2009AA04Z163).

References

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[39]	Ramirez J A, Suarez R, Morales A 2000 Chem. Eng. Sci. 55 3209
[40]	Khalil H K 2008 IEEE International Conference on Control, Automation and Systems xlvii--lvii
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[42]	Sanjay P B, Dennis S B 200 SIAM J. Control Optim. 38 751
[43]	Bacciotti A, Rosier L 2005 Liapunov Functions and Stability in Control Theary (2nd Ed.) (Berlin: Springer-Verlag Berlin Heidelberg) pp175--178
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Cited By

[1]	Chen G R, Lü J H 2003 Dynamics Analysis Control and Synchronization for Lorenz System Family (1st Ed.) (Beijing: Science Press) p1 (in Chinese)[陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (第一版) (北京:科学出版社) 第1页]
[2]	Zou E, Li X F, Chen J G 2002 Chaos Control and Optimize Application (1st Ed.) (Changsha: National Defense University Press) p1 (in Chinese) [邹恩, 李祥飞, 陈建国 2002 混沌控制及其优化应用(第一版) (长沙:国防科技大学出版社) 第1页]
[3]	Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[4]	Zhang J S, Wan J H, Xiao X C 2001 Chin. Phys. 10 97
[5]	Li Z, Han C Z 2001 Chin. Phys. 10 494
[6]	Yu Y G, Zhang S C 2002 Chin. Phys. 11 1249
[7]	Tan W, Wang Y N, Zeng Z F, Huang D, Zhou S W 2004 Chin. Phys. 13 459
[8]	Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 物理学报 54 3502]
[9]	Qi D L 2006 Chin. Phys. 15 1715
[10]	Zheng Y A 2006 Chin. Phys. 15 2549
[11]	Gohary A E, Yassen R 2006 Chaos Soliton. Fract. 29 1085
[12]	Lai X Q, Li Z H, Yuan B, Wang H, Ye Q, Zhao Y R 2010 Acta Phys. Sin. 59 2256 (in Chinese) [来新泉, 李祖贺, 袁冰, 王慧, 叶强, 赵永瑞 2010 物理学报 59 2256]
[13]	Li L X, Peng H P, Guan B Z, Xu J M 2001 Chin. Phys. 10 708
[14]	Fang J Q, Yu X H, Chen G R 2003 Chin. Phys. Lett. 20 2110
[15]	Yu D C, Wu A G, Yang C P 2005 Chin. Phys. 14 914
[16]	Huang L Y, Luo X S, Fang J Q, Zhao Y B, Tang G N 2005 Acta Phys. Sin. 54 543 (in Chinese) [黄良玉, 罗晓曙, 方锦清, 赵益波, 唐国宁 2005 物理学报 54 543]
[17]	Gao Y, Zhou X H, Kong F, Tian J B, Luo W G 2008 J. Huazhong Normal Univ. 42 215 (in Chinese) [高远, 周新红, 孔峰, 田敬北, 罗文广 2008 华中师范大学学报(自然科学版) 42 215]
[18]	He L, Xin X N, He W B, Guo Q 2010 Drive and Control 38 40 (in Chinese) [贺莉, 辛小南, 何文博, 郭强 2010 驱动控制 38 40]
[19]	Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese) [卢伟国, 周雒维, 罗全明, 杜雄 2007 物理学报 56 6275]
[20]	Lü J H, Zhou T S, Zhang S C 2002 Chin. Phys. 11 12
[21]	Li S H, Tian Y P 2003 Chin. Phys. 12 590
[22]	Yue L J, Shen K 2005 Chin. Phys. 14 1760
[23]	Tan W, Wang Y N, Duan F, Li X H 2006 Chin. Phys. 15 2529
[24]	Gao J H, Zheng Z G 2007 Chin. Phys. Lett. 24 359
[25]	Lu W G, Zhou L W, Luo Q M 2007 Chin. Phys. Lett. 24 1837
[26]	Lu W G, Zhou L W, Wu J K 2009 Chin. Phys. Lett. 26 030503
[27]	Ding S H, Li S H 2011 Control and Decision 26 1 (in Chinese) [丁世宏, 李世华 2011 控制与决策 26 1]
[28]	Guo R W 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 255
[29]	Mohammad P A, Hasan P A 2011 Mech. Res. Commun. 38 500
[30]	Yu W G 2010 Phys. Lett. A 374 3021
[31]	Guo R W, Vincent U E 2010 Phys. Lett. A 375 119
[32]	Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728
[33]	Yang X S, Cao J D 2001 Appl. Math. Modell. 34 3631
[34]	Shen J, Cao J D 2011 Cogn. Neurodynamics 5 373
[35]	Zhao J L, Wang J, Wei W 2011 Acta Phys. Sin. 60 100203 (in Chinese) [赵建利, 王京, 魏伟 2011 物理学报 60 100203]
[36]	Zhao J L, Wang J, Wang H 2011 Fourth International Conference on Intelligent Computation Technology and Automation (Washington: IEEE Computer Society) pp333--336
[37]	Luo X S 2007 Theory and Methods of Chaos Control, Synchronization and Its Applications (1st Ed.) (Guilin: Guangxi Normal University Press) p256 (in Chinese) [罗晓曙 2007 混沌控制、同步的理论与方法及其应用(第一版)(桂林:广西师范大学出版社) 第256页]
[38]	Hu J B, Zhuang K Y 2008 Advanced Variable Structure Control Theory and Applications (1st Ed.) (Xi'an: Northwestern Polytechnical University Press) pp53--56 (in Chinese) [胡剑波, 庄开宇 2008 高级变结构控制理论及应用(第一版)(西安:西北工业大学出版社) 第53---56页]
[39]	Ramirez J A, Suarez R, Morales A 2000 Chem. Eng. Sci. 55 3209
[40]	Khalil H K 2008 IEEE International Conference on Control, Automation and Systems xlvii--lvii
[41]	Khalil H K 2007 Nonlinear Systems (3rd Ed.) (Beijing: Publishing House of Electronics Industry) pp443--618
[42]	Sanjay P B, Dennis S B 200 SIAM J. Control Optim. 38 751
[43]	Bacciotti A, Rosier L 2005 Liapunov Functions and Stability in Control Theary (2nd Ed.) (Berlin: Springer-Verlag Berlin Heidelberg) pp175--178
[44]	Zheng D Z 2002 Linear System Theory (2nd Ed.) (Beijing: Tsinghua University Press) pp238--240 (in Chinese) [郑大钟 2002 线性系统理论(第二版) (北京:清华大学出版社) 第238---240页]

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Vol. 61, Issue 11 - 2012-06-05

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