Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

doi:10.1088/1674-1056/22/7/070501

中国物理B ›› 2013, Vol. 22 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/22/7/070501

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

刘平

Shandong Key Laboratory of Gardening Machinery and Equipment, College of Mechanical and Electronic Engineering,Shandong Agricultural University, Taian 271018, China

收稿日期:2012-08-21 修回日期:2012-10-22 出版日期:2013-06-01 发布日期:2013-06-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60874009 and 10971120) and the Natural Science Foundation of Shandong province, China (Grant No. ZR2010FM010).

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

Liu Ping (刘平)

Shandong Key Laboratory of Gardening Machinery and Equipment, College of Mechanical and Electronic Engineering,Shandong Agricultural University, Taian 271018, China

Received:2012-08-21 Revised:2012-10-22 Online:2013-06-01 Published:2013-06-01
Contact: Liu Ping E-mail:pingliu@mail.sdu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60874009 and 10971120) and the Natural Science Foundation of Shandong province, China (Grant No. ZR2010FM010).

摘要/Abstract

摘要： This paper deals with the finite-time stabilization of the unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, the nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple and one of the uncertain unified chaotic complex systems is robust. For the design of finite-time controller on uncertain unified chaotic complex systems, only part of all unknown parameters are required to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and the analysis.

关键词: finite-time stability, uncertain parameters, unified chaotic complex systems

Abstract: This paper deals with the finite-time stabilization of the unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, the nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple and one of the uncertain unified chaotic complex systems is robust. For the design of finite-time controller on uncertain unified chaotic complex systems, only part of all unknown parameters are required to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and the analysis.

Key words: finite-time stability, uncertain parameters, unified chaotic complex systems

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)

刘平. Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters[J]. 中国物理B, 2013, 22(7): 70501-070501.

Liu Ping (刘平). Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters[J]. Chin. Phys. B, 2013, 22(7): 70501-070501.

参考文献 30

[1]	Wang X, Zhang N, Ren X and Zhang Y 2011 Chin. Phys. B 20 020507
[2]	Kolumban G, Kennedy M P and Chua L O 1997 IEEE Trans. Circuits Syst. I 44 927
[3]	Chen G and Dong X 1998 From Chaos to Order: Methodologies Perspectives and Applications (Singapore: World Scientific)
[4]	Chen S H, Liu J, Xie J and Lu J A 2002 Chin. Phys. B 11 233
[5]	Sun F Y 2006 Chin. Phys. Lett. 23 32
[6]	Liu P and Liu S T 2011 Phys. Scr. 83 065006
[7]	Liu S and Liu P 2011 Nonlinear Anal.-Real World Appl. 12 3046
[8]	Guan B, Xu J, Peng H etc 2001 Chin. Phys. B 10 708
[9]	Lü L, Zhang Q L and Guo Z A 2008 Chin. Phys. B 17 498
[10]	Bhat S and Bernstein D 1997 Proceedings of ACC, June 4-6, 1997, NM, Albuquerque, p. 2513
[11]	Haimo V T 1986 SIAM J. Control Optim. 24 760
[12]	Yu W G 2010 Phys. Lett. A 374 3021
[13]	Yu W G 2010 Phys. Lett. A 374 1488
[14]	Millerioux G and Mira C 2001 IEEE Trans. Circuits Syst. I 48 111
[15]	Wang F, Si S and Shi G 2006 Acta Phys. Sin. 55 5694 (in Chinese)
[16]	Yu W 2010 Phys. Lett. A 374 3021
[17]	Guo R and Vincent U E 2010 Phys. Lett. A 375 119
[18]	Gao T, Chen Z and Yuan Z 2005 Acta Phys. Sin. 54 2574 (in Chinese)
[19]	Ning C and Haken H 1990 Phys. Rev. A 41 3826
[20]	Gibbon J D and McGuinnes M J 1982 Physica D 5 108
[21]	Rauh A, Hannibal L and Abraham N 1996 Physica D 99 45
[22]	Hu M, Yang Y, Xu Z and Guo L 2008 Math. Comput. Simul. 79 449
[23]	Wu Z, Duan J and Fu X 2012 Nonlinear Dyn. 69 771
[24]	Rauh A, Hannibal L and Abraham N B 1996 Physica D 99 45
[25]	Mahmoud G M, Bountis T and Mahmoudb E E 2007 Int. J. Bifurc. Chaos 17 4295
[26]	Liu P and Liu S T 2012 Nonlinear Dyn. 70 585
[27]	Liu P and Liu S 2012 Phys. Scr. 85 035005
[28]	Lu J, Chen G, Cheng D and Celikovsky S 2002 Int. J. Bifurc. Chaos 12 2917
[29]	Feng Y, Sun L X and Yu X H 2004 The 30th Annual Conference of the IEEE Industrial Electronics Society, November 2-6, 2004, Busan, Korea, p. 2911
[30]	Khalil H K 2002 Nonlinear Systems 3rd edn. (New Jersey: Prentice-Hall)

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 30

相关文章 9

Metrics

本文评价

推荐阅读 0

[1]	李树凯, 杨立兴, 李克平. Robust output feedback cruise control for high-speed train movement with uncertain parameters[J]. , 2015, 24(1): 10503-010503.
[2]	柴元, 陈立群. Periodic synchronization of community networks with non-identical nodes uncertain parameters and adaptive coupling strength[J]. 中国物理B, 2014, 23(3): 30504-030504.
[3]	Mohammad Pourmahmood Aghababa, Hasan Pourmahmood Aghababa . Chaos suppression of uncertain gyros in a given finite time[J]. 中国物理B, 2012, 21(11): 110505-110505.
[4]	桑金玉, 杨吉, 岳立娟. Complete synchronization of double-delayed R"ossler systems with uncertain parameters[J]. 中国物理B, 2011, 20(8): 80507-080507.
[5]	赵辉, 马亚军, 刘思佳, 高士根, 钟丹. Controlling chaos in power system based on finite-time stability theory[J]. 中国物理B, 2011, 20(12): 120501-120501.
[6]	胡佳, 张群娇. Adaptive synchronization of uncertain Liu system via nonlinear input[J]. 中国物理B, 2008, 17(2): 503-506.
[7]	齐冬莲. Adaptive passive equivalence of uncertain Lü system[J]. 中国物理B, 2006, 15(8): 1715-1718.
[8]	李智, 韩崇昭. Global adaptive synchronization of chaotic systems with uncertain parameters[J]. 中国物理B, 2002, 11(1): 9-11.
[9]	李智, 韩崇昭. ADAPTIVE CONTROL AND IDENTIFICATION OF CHAOTIC SYSTEMS[J]. 中国物理B, 2001, 10(6): 494-496.