一种分数阶混沌系统同步的自适应滑模控制器设计

潘光; 魏静

doi:10.7498/aps.64.040505

摘要

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.

关键词:

In this paper, the synchronization of fractional-order chaotic systems is investigated. Based on sliding mode control and adaptive control theory, a fractional order integral sliding surface with strong robustness is designed, and an adaptive sliding controller is proposed for synchronizing the fractional-order chaotic systems with retaining the nonlinear part. Numerical simulations on synchronizing the Chen chaotic systems, the Liu chaotic systems, and Arneodo chaotic systems are carried out separately. The simulation results show the validity and feasibility of the adaptive sliding controller.

Keywords:

作者及机构信息

潘光,
魏静

1.
西北工业大学航海学院, 西安 710072

Authors and contacts

Pan Guang,
Wei Jing

1.
College of Marine Engineering, Northwestern Polytechnical University, Xi'an 710072, China

参考文献

[1]	Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2]	Ditto W L, Rauseo S N, Spano M L 1990 Phys. Rev. Lett. 65 3211
[3]	Chen S, L J 2002 Chaos Solition. Fract. 14 643
[4]	Wang C, Su J 2004 Chaos Solition. Fract. 20 967
[5]	Gao X, Yu J B 2005 Chaos Solition. Fract. 26 141
[6]	Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[7]	Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[8]	Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 物理学报 61 160510]
[9]	Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]
[10]	Yu Y G, Wen G G, Li H X, Diao M 2009 Int. J. Nonlinear Sci. Num. 10 379
[11]	Faieghi M R, Delavari H 2012 Commum. Nolinear Sci. Numer. Simulat. 17 731
[12]	Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[13]	Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[14]	Deng W H 2007 Phys. Rev.E 75 056201
[15]	Li Z, Han C Z 2002 Chin. Phys. 11 666
[16]	Mohammad S T, Mohammad H 2008 Physica A 387 57
[17]	Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若徇 2011 物理学报 60 050510]
[18]	Wu X J, Li J, Chen G R 2008 J. Franklin Institute 345 392
[19]	Ahamd W M, Sprott J C 2003 Chaos Soliton. Fract. 16 339
[20]	Sun K H, Ren J, Shang F 2008 Comput. Simulat. 25 312 (in Chinese) [孙克辉, 任健, 尚芳 2008 计算机仿真 25 312]
[21]	Liu C X, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[22]	Lu J G 2005 Chaos Soliton. Fract. 26 1125

施引文献

[1]	Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[2]	Ditto W L, Rauseo S N, Spano M L 1990 Phys. Rev. Lett. 65 3211
[3]	Chen S, L J 2002 Chaos Solition. Fract. 14 643
[4]	Wang C, Su J 2004 Chaos Solition. Fract. 20 967
[5]	Gao X, Yu J B 2005 Chaos Solition. Fract. 26 141
[6]	Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[7]	Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[8]	Huang L L, Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese) [黄丽莲, 马楠 2012 物理学报 61 160510]
[9]	Niu H, Zhang G S 2013 Acta Phys. Sin. 62 130502 (in Chinese) [牛弘, 张国山 2013 物理学报 62 130502]
[10]	Yu Y G, Wen G G, Li H X, Diao M 2009 Int. J. Nonlinear Sci. Num. 10 379
[11]	Faieghi M R, Delavari H 2012 Commum. Nolinear Sci. Numer. Simulat. 17 731
[12]	Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[13]	Li C P, Deng W H 2006 Int. J. Modern Phys. B 20 791
[14]	Deng W H 2007 Phys. Rev.E 75 056201
[15]	Li Z, Han C Z 2002 Chin. Phys. 11 666
[16]	Mohammad S T, Mohammad H 2008 Physica A 387 57
[17]	Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若徇 2011 物理学报 60 050510]
[18]	Wu X J, Li J, Chen G R 2008 J. Franklin Institute 345 392
[19]	Ahamd W M, Sprott J C 2003 Chaos Soliton. Fract. 16 339
[20]	Sun K H, Ren J, Shang F 2008 Comput. Simulat. 25 312 (in Chinese) [孙克辉, 任健, 尚芳 2008 计算机仿真 25 312]
[21]	Liu C X, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[22]	Lu J G 2005 Chaos Soliton. Fract. 26 1125

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