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针对异结构不同维分数阶混沌系统的广义同步问题进行研究, 设计了一种将滑模变结构理论和自适应控制理论相结合的方法.通过设计一种对外界干扰具有强鲁棒性的分数阶滑模面, 以及构造合适的自适应滑模控制器, 该控制器将系统的运动控制到滑模面上, 使系统轨道沿滑动模运动到所需的控制状态, 最终实现了两个不同维异结构混沌系统之间的广义同步.以四维超混沌Chen系统和三维Chen混沌系统为例, 对这两个系统分别进行升维和降维的同步仿真. 仿真模拟结果表明, 运用本文设计的控制器, 经过短暂的时间, 两系统的广义误差变量始终平稳地趋于零, 即证明了这种控制器的有效性.In this paper, based on sliding mode control and adaptive control theory, the synchronization of two different fractional order chaotic systems is investigated. First, a fractional sliding surface with strong robustness is designed and a suitable adaptive sliding controller is constructed, then the error states of the systems are controlled to the sliding surface via the method to guarantee the synchronized behaviors between two fractional chaotic systems. Numerical simulations on the hyper Chen chaotic systems and Chen chaotic system are also carried out respectively. Simulation results show that the generalized errors tend to zero after a short time, and the effectiveness and feasibility of this method are well verified.
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Keywords:
- fractional order chaotic systems /
- different-structure /
- adaptive sliding mode control /
- chaos synchronization
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[2] Li X J, Liu J, Dong P Z, Xing L F 2009 J. Wuhan Univ. Sci. Engin. 22 30
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[16] Wu X J, Li J, Chen G R 2008 J. Franklin Institue 345 392
[17] Zhang H, Ma X K, Yang Y, Xu C D 2005 Chin. Phys. 14 86
[18] Li H Y, Hu Y A 2011 Commun. Nolinear Sci. Numer. Simulat. 16 3904
[19] Shao S Q, Gao X, Liu X W 2007 Acta Phys. Sin. 56 6815 (in Chinese) [邵仕泉,高心,刘兴文2007 物理学报 56 6815]
[20] Faieghi M R, Delavari H 2012 Commun. Nolinear Sci. Numer. Simulat. 17 731
[21] Zhu H, Zhou S B, He Z S 2009 Chaos Soliton. Fract. 41 2733
[22] Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[23] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元,王明军2007 物理学报 56 6843]
[24] Zhang G, Liu Z R, Ma Z J 2007 Chaos Soliton. Fract. 32 773
[25] Bowong S, McClintock V E P 2006 Phys. Lett. A 358 134
[26] Wang F Q, Liu C X 2005 J. North China Eletric Power Univ. 32 11 (in Chinese) [王发强,刘崇新2005 华北电力大学学报 32 11]
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[1] Podlubny I 1999 Fractional Differential Equations (New York:Academic Press)
[2] Li X J, Liu J, Dong P Z, Xing L F 2009 J. Wuhan Univ. Sci. Engin. 22 30
[3] Qiao Z M, Jin Y R 2010 J. Anhui Univ. (Natural Science Edition) 34 23
[4] Zhang R X, Yang S P 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵,杨世平 2010 物理学报 59 1549]
[5] Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524 (in Chinese) [许喆,刘崇新,杨韬2010 物理学报 59 1524]
[6] Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[7] Zhang H G, Fu J, Ma T D, Tong S C 2009 Chin. Phys. B 18 969
[8] Kuang J Y, Deng K, Huang R H 2001 Acta Phys. Sin. 50 1856 (in Chinese) [匡锦瑜,邓昆,黄荣怀2001 物理学报 50 1856]
[9] Liu F, Ren Y, Shan X M, Qiu Z L 2002 Chaos Soliton. Fract. 13 723
[10] Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 5055 (in Chinese) [王发强,刘崇新2006 物理学报 55 5055]
[11] Gao X, Yu J B 2005 Chaos Soliton. Fract. 26 141
[12] Li G H 2004 Acta Phys. Sin. 53 999 (in Chinese) [李国辉2004 物理学报 53 999]
[13] Li Z, Han C Z 2002 Chin. Phys. 11 666
[14] 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]
[15] Mohammad S T, Mohammad H 2008 Physica A:Statist. Mech. Appl. 387 57
[16] Wu X J, Li J, Chen G R 2008 J. Franklin Institue 345 392
[17] Zhang H, Ma X K, Yang Y, Xu C D 2005 Chin. Phys. 14 86
[18] Li H Y, Hu Y A 2011 Commun. Nolinear Sci. Numer. Simulat. 16 3904
[19] Shao S Q, Gao X, Liu X W 2007 Acta Phys. Sin. 56 6815 (in Chinese) [邵仕泉,高心,刘兴文2007 物理学报 56 6815]
[20] Faieghi M R, Delavari H 2012 Commun. Nolinear Sci. Numer. Simulat. 17 731
[21] Zhu H, Zhou S B, He Z S 2009 Chaos Soliton. Fract. 41 2733
[22] Wang X Y, He Y J 2008 Phys. Lett. A 372 435
[23] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元,王明军2007 物理学报 56 6843]
[24] Zhang G, Liu Z R, Ma Z J 2007 Chaos Soliton. Fract. 32 773
[25] Bowong S, McClintock V E P 2006 Phys. Lett. A 358 134
[26] Wang F Q, Liu C X 2005 J. North China Eletric Power Univ. 32 11 (in Chinese) [王发强,刘崇新2005 华北电力大学学报 32 11]
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