Stochastic impulsive control for the stabilization of Lorenz system

doi:10.1088/1674-1056/20/2/020506

Abstract This paper derives some sufficient conditions for the stabilization of Lorenz system with stochastic impulsive control. The estimate of the upper bound of impulse interval for asymptotically stable control is obtained. Some differences between the system with stochastic impulsive control and with deterministic impulsive control are presented. Computer simulation is given to show the effectiveness of the proposed method.

Keywords: stabilization Lorenz system stochastic impulsive control

Received: 22 October 2009
Revised: 25 August 2010
Accepted manuscript online:

PACS:

05.45.Gg

(Control of chaos, applications of chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10872165).

Cite this article:

Wang Liang(王亮), Zhao Rui(赵锐), Xu Wei(徐伟), and Zhang Ying(张莹) vgluept Stochastic impulsive control for the stabilization of Lorenz system 2011 Chin. Phys. B 20 020506

[1]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2]	Cao Y J 2007 Phys. Lett. A 270 171
[3]	Cai G L, Zheng S and Tian L X 2008 Chin. Phys. B 17 2412
[4]	Wang Y W, Guan Z H and Wang H O 2003 Phys. Lett. A 312 34
[5]	Huang D B 2005 Phys. Rev. E 71 037203
[6]	Yang T 1999 IEEE Trans. Automat. Control 44 1081
[7]	Yang T, Yang L B and Yang C M 1997 Physica D 110 18
[8]	Yang T, Yang L B and Yang C M 1997 Phys. Lett. A 226 349
[9]	Xie W X, Wen C Y and Li Z G 2000 Phys. Lett. A 275 67
[10]	Chen D L, Sun J T and Huang C S 2006 Chaos, Solitons and Fractals 28 213
[11]	Wu X Q, Lu J A, Tse C K, Wang J J and Liu J 2007 Chaos, Solitons and Fractals 31 631
[12]	Wang Y W, Guan Z H and Xiao J W 2004 Chaos 14 199
[13]	Wang L, Xu W and Li Y 2008 Phys. Lett. A 372 5309
[14]	Peng S G and Yu S M 2009 Chin. Phys. B 18 3758
[15]	Zhang H G, Fu J, Ma T D and Tong S C 2009 Chin. Phys. B 18 969
[16]	Liu X W, Huang Q Z, Gao X and Shao S Q 2007 Chin. Phys. 16 2272
[17]	Zhang X H and Li D 2009 Chin. Phys. B 18 1774
[18]	Lorenz E N 1963 J Atmos. Sci. 20 130 endfootnotesize

[1]	Tailoring of thermal expansion and phase transition temperature of ZrW₂O₈ with phosphorus and enhancement of negative thermal expansion of ZrW_1.5P_0.5O_7.75 Chenjun Zhang(张晨骏), Xiaoke He(何小可), Zhiyu Min(闵志宇), and Baozhong Li(李保忠). Chin. Phys. B, 2023, 32(4): 048201.
[2]	Generation of stable and tunable optical frequency linked to a radio frequency by use of a high finesse cavity and its application in absorption spectroscopy Yueting Zhou(周月婷), Gang Zhao(赵刚), Jianxin Liu(刘建鑫), Xiaojuan Yan(闫晓娟), Zhixin Li(李志新), Weiguang Ma(马维光), and Suotang Jia(贾锁堂). Chin. Phys. B, 2022, 31(6): 064206.
[3]	Dynamics and intermittent stochastic stabilization of a rumor spreading model with guidance mechanism in heterogeneous network Xiaojing Zhong(钟晓静), Yukun Yang(杨宇琨), Runqing Miao(苗润青), Yuqing Peng(彭雨晴), and Guiyun Liu(刘贵云). Chin. Phys. B, 2022, 31(4): 040205.
[4]	Dynamic stabilization of atomic ionization in a high-frequency laser field with different initial angular momenta Di-Yu Zhang(张頔玉), Yue Qiao(乔月), Wen-Di Lan(蓝文迪), Jun Wang(王俊), Fu-Ming Guo(郭福明), Yu-Jun Yang(杨玉军), and Da-Jun Ding(丁大军). Chin. Phys. B, 2022, 31(10): 103202.
[5]	Spectral filtering of dual lasers with a high-finesse length-tunable cavity for rubidium atom Rydberg excitation Yang-Yang Liu(刘杨洋), Zhuo Fu(付卓), Peng Xu(许鹏), Xiao-Dong He(何晓东), Jin Wang(王谨), and Ming-Sheng Zhan(詹明生). Chin. Phys. B, 2021, 30(7): 074203.
[6]	Discontinuous event-trigger scheme for global stabilization of state-dependent switching neural networks with communication delay Yingjie Fan(樊英杰), Zhen Wang(王震), Jianwei Xia(夏建伟), and Hao Shen(沈浩). Chin. Phys. B, 2021, 30(3): 030202.
[7]	Stabilization strategy of a car-following model with multiple time delays of the drivers Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.
[8]	High-performance frequency stabilization of ultraviolet diode lasers by using dichroic atomic vapor spectroscopy and transfer cavity Danna Shen(申丹娜), Liangyu Ding(丁亮宇), Qiuxin Zhang(张球新), Chenhao Zhu(朱晨昊), Yuxin Wang(王玉欣), Wei Zhang(张威), Xiang Zhang(张翔). Chin. Phys. B, 2020, 29(7): 074210.
[9]	Stable continuous-wave single-frequency intracavity frequency-doubled laser with intensity noise suppressed in audio frequency region Ying-Hao Gao(高英豪), Yuan-Ji Li(李渊骥), Jin-Xia Feng(冯晋霞), Kuan-Shou Zhang(张宽收). Chin. Phys. B, 2019, 28(9): 094204.
[10]	Non-crossover sub-Doppler DAVLL in selective reflection scheme Lin-Jie Zhang(张临杰), Hao Zhang(张好), Yan-Ting Zhao(赵延霆), Lian-Tuan Xiao(肖连团), Suo-Tang Jia(贾锁堂). Chin. Phys. B, 2019, 28(8): 084211.
[11]	Flexible control of semiconductor laser with frequency tunable modulation transfer spectroscopy Ning Ru(茹宁), Yu Wang(王宇), Hui-Juan Ma(马慧娟), Dong Hu(胡栋), Li Zhang(张力), Shang-Chun Fan(樊尚春). Chin. Phys. B, 2018, 27(7): 074201.
[12]	Dynamic stabilization of Na atom in an intense pulsed laser field Xiao-Li Guo(郭晓丽), Song-Feng Zhao(赵松峰), Guo-Li Wang(王国利), Xiao-Xin Zhou(周效信). Chin. Phys. B, 2018, 27(4): 043201.
[13]	Modulation transfer spectroscopy based on acousto-optic modulator with zero frequency shift Chen-Fei Wu(吴晨菲), Xue-Shu Yan(颜学术), Li-Xun Wei(卫立勋), Pei Ma(马沛), Jian-Hui Tu(涂建辉), Jian-Wei Zhang(张建伟), Li-Jun Wang(王力军). Chin. Phys. B, 2018, 27(11): 114203.
[14]	Stabilizing effect of plasma discharge on bubbling fluidized granular bed Hu Mao-Bin (胡茂彬), Dang Sai-Chao (党赛超), Ma Qiang (马强), Xia Wei-Dong (夏维东). Chin. Phys. B, 2015, 24(7): 074502.
[15]	A long-term frequency-stabilized erbium-fiber-laser-based optical frequency comb with an intra-cavity electro-optic modulator Zhang Yan-Yan (张颜艳), Yan Lu-Lu (闫露露), Zhao Wen-Yu (赵文宇), Meng Sen (孟森), Fan Song-Tao (樊松涛), Zhang Long (张龙), Guo Wen-Ge (郭文阁), Zhang Shou-Gang (张首刚), Jiang Hai-Feng (姜海峰). Chin. Phys. B, 2015, 24(6): 064209.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Stochastic impulsive control for the stabilization of Lorenz system

Cite this article:

Online attention