Cascade adaptive control of uncertain unified chaotic systems

doi:10.1088/1674-1056/20/4/040510

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40510-040510.doi: 10.1088/1674-1056/20/4/040510

Cascade adaptive control of uncertain unified chaotic systems

王京¹, 魏伟², 李东海³

(1)Engineering Research Institute, University of Science and Technology Beijing, Beijing 100083, China; (2)School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China; (3)State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

收稿日期:2010-09-06 修回日期:2010-11-18 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the National Basic Research Program of China (Grant No. 2007CB210106).

Cascade adaptive control of uncertain unified chaotic systems

Wei Wei(魏伟)^a)†, Li Dong-Hai(李东海)^b), and Wang Jing(王京)^c)

^a School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China; ^b State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China; ^c Engineering Research Institute, University of Science and Technology Beijing, Beijing 100083, China

Received:2010-09-06 Revised:2010-11-18 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the National Basic Research Program of China (Grant No. 2007CB210106).

摘要/Abstract

摘要： The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point. Since an adaptive controller based on dynamic compensation mechanism is employed, the exact model of the unified chaotic system is not necessarily required. By choosing appropriate controller parameters, chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.

关键词: unified chaotic systems, cascade adaptive control approach, response speed, chaos control

Abstract: The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point. Since an adaptive controller based on dynamic compensation mechanism is employed, the exact model of the unified chaotic system is not necessarily required. By choosing appropriate controller parameters, chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.

Key words: unified chaotic systems, cascade adaptive control approach, response speed, chaos control

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

05.45.Gg

魏伟, 李东海, 王京. Cascade adaptive control of uncertain unified chaotic systems[J]. 中国物理B, 2011, 20(4): 40510-040510.

Wei Wei(魏伟), Li Dong-Hai(李东海), and Wang Jing(王京). Cascade adaptive control of uncertain unified chaotic systems[J]. Chin. Phys. B, 2011, 20(4): 40510-040510.

参考文献 32

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Chua L O, Komuro M and Matsumoto T 1986 IEEE Trans. Circ. Sys. 33 1072
[3]	Chen G and Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[4]	Ueta T and Chen G 2000 Int. J. Bifur. Chaos 10 1917
[5]	Lü J H and Chen G 2002 Int. J. Bifur. Chaos 12 659
[6]	Liu C X, Liu T, Liu L and Liu K 2004 Chaos, Solitions and Fractals 22 1031
[7]	Lü J H, Chen G, Chen D Z and Serget C 2002 Int. J. Bifur. Chaos 12 2917
[8]	Chen G and Dong X 1998 From Chaos to Order: Methodologies, Perspectives and Applications (Singapore: World Scientific)
[9]	Ogorzalek M J 1997 Chaos and Complexity in Nonlinear Electronic Circuits (Singapore: World Scientific)
[10]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 64 1196
[11]	Pyragas K 1992 Phys. Lett. A 170 421
[12]	Lü J H and Lu J A 2003 Chaos, Solitons and Fractals 17 127
[13]	Rafikov M and Balthazar J M 2008 Commun. Nonlinear Sci. Numer. Simul. 13 1246
[14]	Chen M Y, Zhou D H and Shang Y 2004 Chaos, Solitons and Fractals 21 295
[15]	Ge S S, Wang C and Lee T H 2000 Int. J. Bifur. Chaos 10 1149
[16]	Wang C and Ge S S 2001 Int. J. Bifur. Chaos 11 1115
[17]	Chen S H, Yang Q and Wang C P 2004 Chaos, Solitons and Fractals 20 751
[18]	Liu J, Chen S H and Xie J 2004 Chaos, Solitons and Fractals 19 533
[19]	Hua C C, Guan X P and Shi P 2005 Chaos, Solitons and Fractals 23 757
[20]	Gao X and Liu X W 2007 Acta Phys. Sin. 56 84 (in Chinese)
[21]	Chen B, Liu X P and Tong S C 2007 Chaos, Solitons and Fractals 34 1180
[22]	Wang F Q and Liu C X 2007 Physica D 225 55
[23]	Chen X R and Liu C X 2010 Nonlinear Analysis: Real World Applications 11 683
[24]	Chiang T Y, Hung M L, Yan J J, Yang Y S and Chang J F 2007 Chaos, Solitons and Fractals 34 437
[25]	Mohamed Z, Nejib S and Haitham S 2009 Chaos, Solitons and Fractals 42 3197
[26]	Duan Z S and Chen G R 2009 IEEE Trans. CAS-II 56 679
[27]	Wang H, Han Z Z, Zhang W and Xie Q Y 2009 Nonlinear Analysis: Real World Applications 10 715
[28]	Wang H, Han Z Z, Xie Q Y and Zhang W 2009 Nonlinear Analysis: Real World Applications 10 2842
[29]	Chen G R and Lü J H 2003 Dynamics Analysis, Control and Synchronization of Generalized Lorenz System (Beijing: Science Press)
[30]	Tornambe A and Valigi P 1994 ASME J. Dyn. Syst. Meas. Control 116 293
[31]	Xu Y, Li D H, Lao D Z and Song Y J 2008 J. Syst. Simul. 20 2666 (in Chinese)
[32]	Liu Y Z and Fei S M 2005 Acta Phys. Sin. 54 3486 (in Chinese) endfootnotesize

Cascade adaptive control of uncertain unified chaotic systems

Cascade adaptive control of uncertain unified chaotic systems

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Control of chaos in Frenkel-Kontorova model using reinforcement learning[J]. 中国物理B, 2021, 30(5): 50503-050503.
[2]	高飞, 李文琴, 童恒庆, 李喜玲. Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system[J]. 中国物理B, 2019, 28(9): 90501-090501.
[3]	赵岩, 李成龙, 沈亮. Recent research process on perovskite photodetectors:A review for photodetector – materials, physics, and applications[J]. 中国物理B, 2018, 27(12): 127806-127806.
[4]	庞明宝, 黄玉满. Coordinated chaos control of urban expressway based on synchronization of complex networks[J]. 中国物理B, 2018, 27(11): 118902-118902.
[5]	Marius-F Danca, Wallace K S Tang. Parrondo's paradox for chaos control and anticontrol of fractional-order systems[J]. 中国物理B, 2016, 25(1): 10505-010505.
[6]	李天增, 王瑜, 罗懋康. Control of fractional chaotic and hyperchaotic systems based on a fractional order controller[J]. , 2014, 23(8): 80501-080501.
[7]	殷久利, 赵刘威, 田立新. Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity[J]. 中国物理B, 2014, 23(2): 20204-020204.
[8]	李瑞红, 陈为胜. Complex dynamical behavior and chaos control for fractional-order Lorenz-like system[J]. Chin. Phys. B, 2013, 22(4): 40503-040503.
[9]	Hossein Gholizadeh, Amir Hassannia, Azita Azarfar. Chaos detection and control in a typical power system[J]. Chin. Phys. B, 2013, 22(1): 10503-010503.
[10]	张路, 邓科, 罗懋康. Control of fractional chaotic system based on fractional-order resistor–capacitor filter[J]. 中国物理B, 2012, 21(9): 90505-090505.
[11]	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.
[12]	陈帝伊, 刘玉晓, 马孝义, 张润凡. No-chattering sliding mode control in a class of fractional-order chaotic systems[J]. 中国物理B, 2011, 20(12): 120506-120506.
[13]	张若洵, 杨世平. Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller[J]. 中国物理B, 2011, 20(11): 110506-110506.
[14]	冯玉玲, 张喜和, 姚治海. Chaotic behaviours and control of chaos in the p－Ge photoconductor[J]. 中国物理B, 2010, 19(6): 60511-060511.
[15]	张小洪, 李东. Fuzzy modeling and impulsive control of hyperchaotic Lü system[J]. 中国物理B, 2009, 18(5): 1774-1779.