Journal of Shandong University(Engineering Science) ›› 2018, Vol. 48 ›› Issue (5): 91-94, 123.doi: 10.6040/j.issn.1672-3961.0.2017.614

• Control Science & Engineering • Previous Articles     Next Articles

Synchronization control of fractional-order multi-scroll chaotic system based on reduced-order method

Chunyan WANG(),Jinhong DI   

  1. College of Electronic Communication Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China
  • Received:2017-12-14 Online:2018-10-01 Published:2017-12-14
  • Supported by:
    河南省科技攻关计划资助项目(172102210080)

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Abstract:

The problem of synchronization control of intergal-order and fractional-order multi-scroll chaotic systems were studied based on reduced-order method. Third fractional-order multi-scroll system was transferred into a first-order system. The chaotic synchronization sufficient conditions were arrived for the drive-response systems of fractional-order multi-scroll system which acquired synchronization using fractional-order Lyapunov. The strict proof in mathematics was given out, and the simulations examples demonstrated the efficient of the proposed method.

Key words: fractional-order, multi-scroll systems, reduced-order, synchronization

CLC Number: 

  • O482.4

Fig.1

The system error curves of theorem1"

Fig.2

The system error curves of theorem2"

1 毛北行, 程春蕊. 分数阶Victor-Carmen混沌系统的自适应滑模同步同步[J]. 山东大学学报(工学版), 2017, 47 (4): 31- 36.
MAO Beixing , CHENG Chunrui . Self-adaptive synchronization of sliding mode control of fractional order Victor-Carmen chaotic system[J]. Journal of Shandong University (Engineering Science), 2017, 47 (4): 31- 36.
2 单梁, 李军, 王执拴. 一个新的分段线性混沌系统的反馈同步[J]. 南京理工大学学报, 2007, 31 (3): 265- 269.
doi: 10.3969/j.issn.1005-9830.2007.03.001
SHAN Liang , LI Jun , WANG Zhishuan . Feedback synchronization of a new piecewise chaotic systems[J]. Journal of Nanjing University of Science and Technology, 2007, 31 (3): 265- 269.
doi: 10.3969/j.issn.1005-9830.2007.03.001
3 ZENG Yanhui , LUO Runzi , SU Haipeng . The control of a class of uncertain fractional-order chaotic systems via reduced order method[J]. Optic, 2016, 127, 11948- 11959.
4 ZHANG Yi . Fractional differential equations of motion interms of combined riemann-liouville derivatives[J]. Chinese Physics B, 2012, 8 (21): 302- 306.
5 SALARIEH H , ALASTY A . Adaptive synchronization of two chaotic systems with stochastic unknown parameters[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14 (2): 508- 519.
doi: 10.1016/j.cnsns.2007.09.002
6 SUN Y P , LI J M , WANG J A , et al. Generalized projective synchronization of chaotic systems via adaptive learning control[J]. Chinese Physics B, 2010, 19 (2): 502- 505.
7 LIU P , LIU S . Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances[J]. Nonlinear Dynamics, 2012, 70 (1): 585- 599.
doi: 10.1007/s11071-012-0479-y
8 YANG L , YANG J . Robust finite-time convergence of chaotic systems via adaptive terminal sliding mode scheme[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16 (6): 2405- 2413.
doi: 10.1016/j.cnsns.2010.09.022
9 SHAHIRI M , GHADRI R , RANJBAR N , et al. Chaotic fractional-order coulletsystem: Synchronization and control approach[J]. Commun Nonlinear Sci Numer Simul, 2010, 45 (3): 665- 674.
10 HAMAMCI S E , KOLKSAL M . Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems[J]. Comput Math Appl, 2010, 52 (2): 1267- 1278.
11 MEI Jun , JIANG Minghui , WANG Jun . Finite-time structure identification and synchronization of drive-response systems with uncertain parameter[J]. Commun Nonlinear Sci Numer Simulat, 2013, (18): 999- 1015.
12 毛北行, 李巧利. 一类分数阶Duffling-Van der pol系统的混沌同步[J]. 吉林大学学报(自然科学版), 2016, 54 (2): 369- 373.
MAO Beixing , LI Qiaoli . Chaos synchronization of a class of fractional-order Duffling-Van der pol systems[J]. Journal of Jilin University(Naturnal Science Edition), 2016, 54 (2): 369- 373.
13 YU Jinyong , LEI Junwei . Synchronization of chaotic system with adaptive transfer function sliding mode method[J]. Optic, 2017, 132, 209- 319.
14 LU J G . Chaotic dynamics and cynchronization of fractional-order Genesio-Tesi systems[J]. Chinese Physics, 2005, 14 (8): 1517- 1521.
doi: 10.1088/1009-1963/14/8/007
15 毛北行, 李巧利. 一类分数阶Genesio-Tesi系统的滑模混沌同步[J]. 中山大学学报(自然科学版), 2017, 56 (2): 76- 79.
MAO Beixing , LI Qiaoli . Sliding mode chaos synchronization of a class of fractional-order Genesio-Tesi systems[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2017, 56 (2): 76- 79.
16 刘晓君, 洪灵. 分数阶Genesio-Tesi系统的混沌及自适应同步[J]. 动力学与控制学报, 2016, 14 (4): 318- 323.
LIU Xiaojun , HONG Ling . Chaos and adaptive synchronization in fractional-order Genesio-Tesi systems[J]. Journal of Dynamics and Control, 2016, 14 (4): 318- 323.
17 毛北行, 孟晓玲. 具有死区输入的分数阶多涡卷混沌系统的有限时间同步[J]. 浙江大学学报(理学版), 2017, 44 (3): 302- 305.
MAO Beixing , MENG Xiaoling . Finite-time synchronization of fractional-order multi-scroll systems with dead-zone input[J]. Journal of Zhejiang University (Science Edition), 2017, 44 (3): 302- 305.
18 毛北行, 王东晓. 分数阶多涡卷系统滑模控制混沌同步[J]. 山东大学学报(工学版), 2017, 47 (3): 79- 83.
MAO Beixing , WANG Dongxiao . Sliding mode chaos synchronization control of a class of fractional-order multi-scroll systems[J]. Journal of Shandong University(Engineering Science), 2017, 47 (3): 79- 83.
19 POD L B . Fractional differential equation[M]. San Diego, CA, USA: Academic Press, 1999.
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