JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2017, Vol. 47 ›› Issue (3): 79-83.doi: 10.6040/j.issn.1672-3961.0.2016.058

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Sliding model chaos synchronization control of a class of fractional-order multi-scroll systems

MAO Beixing, WANG Dongxiao   

  1. College of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China
  • Received:2016-02-18 Online:2017-06-20 Published:2016-02-18

Abstract: The problem of sliding model chaos synchronization of a class of fractional-order multi-scroll systems with certain and uncertain parameter was studied based on fractional order calculus theory and sliding mode control approach. The switching function and controller was designed, two sufficient conditions were arrived for the fractional order systems sliding model synchronization. The research conclusion illustrated that fractional-order multi-scroll systems was sliding mode chaos synchronization under proper controllers and self-adaptive law.

Key words: fractional-order, multi-scroll system, chaos synchronization, sliding model

CLC Number: 

  • O482.4
[1] YASSEN M T. Controlling chaos and synchronization for new chaotic system using linear feedback control[J].Chaos,Solition & Fractals, 2005, 26(3):913-920.
[2] CHEN M, CHEN W. Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems[J]. Chaos, Solition & Fractals, 2009, 41(5):2716-2724.
[3] PECORA L M, CAROLL T L. Synchronization in chaotic systems[J]. Physics Review Letters, 1990, 64(8):821-824.
[4] WU X J, LU H T. Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters[J]. Chaos, Solition & Fractals, 2011, 44(10):820-810.
[5] SALARIEH H, ALASTY A. Adaptive synchronization of two chaotic systems with with stochastic unknown parameters[J].Communications in Nonlinear Science and Numerical Simulation, 2009, 14(2):508-519.
[6] SUN Y P, LI J M, WANG J A, et al. Generalized projective synchronization of chaotic systems via adaptive learing control[J].Chinese Physics B, 2010, 19(2):502-505.
[7] 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.
[8] AGHABABA M P, AKBARI M E. A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances[J].Applied Mathematics and Computation, 2012, 218(9):5757-5768.
[9] AGHABABA M P, HEYDARI A. Chaos synchronization between two different chaotic systems with uncertainties,external disturbances,unknown parameters and input nonlinearities[J].Applied Mathematical Modlling, 2012, 36(4):1639-1652.
[10] LIU P, LIU S. Robust adaptive full state hybrid synchronization of chaotic complex systems with unkown parameters and external disturbances[J].Nonlinear Dynamics, 2012, 70(1):585-599.
[11] 毛北行,张玉霞. 具有非线性耦合复杂网络混沌系统的有限时间同步[J].吉林大学学报(理学版),2015,53(4):757-761. MAO Beixing, ZHANG Yuxia. Finite-time chaos synchronization of complex networks systems with nonlinear coupling[J].Journal of Jilin University(Science Edition), 2015, 53(4):757-761.
[12] 孙宁,张化光,王智良. 不确定分数阶混沌系统的滑模投影同步[J].浙江大学学报(工学版),2010,44(7):1288-1291. SUN Ning, ZHANG Huaguang, WANG Zhiliang. Projective synchronization of uncertain fractional order chaotic system using sliding mode controller[J].Journal of Zhejiang University(Engineering Science Edition), 2010, 44(7):1288-1291.
[13] 余明哲,张友安. 一类不确定分数阶混沌系统的滑模自适应同步[J].北京航空航天大学学报,2014,40(9):1276-1280. YU Mingzhe, ZHANG Youan. Sliding mode adaptive synchronization for a class of fractional-orderchaotic systems with uncertainties[J].Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(9):1276-1280.
[14] 仲启龙,邵永辉,郑永爱. 分数阶混沌系统的主动滑模同步[J].动力学与控制学报,2015,13(1):18-22. ZHONG Qilong, SHAO Yonghui, ZHENG Yongai. Synchronization of the fractional order chaotic systems based on TS Models[J]. Journal of Dynamics and Control, 2015, 13(1):18-22.
[15] 张燕兰. 分数阶Rayleigh-Duffling-like系统的自适应追踪广义投影同步[J].动力学与控制学报,2014,12(4):348-352. ZHANG Yanlan. Adaptive tracking generalized projective synchronization of fractional Rayleigh-Duffling-like system[J].Journal of Dynamics and Control, 2014, 12(4):348-352.
[16] 王震,吴云天,邹永杰. 多涡卷Jerk电路混沌系统的分析与滑模控制[J].西安电子科技大学学报,2009,27(6):765-768. WANG Zhen, WU Yuntian, ZOU Yongjie. Analysis and sliding control of multi-scroll jerk circuit chaotic system[J]. Journal of Xi'an University of Science and Technology, 2009, 27(6):765-768.
[17] 刘恒,余海军,向伟. 带有未知扰动的多涡卷混沌系统修正函数时滞投影同步[J].物理学报,2012,61(18):5031-5036. LIU Heng, YU Haijun, XIANG Wei. Modified function projective lag synchronization for multi-scroll chaotic system with unknown disturbances[J]. Acta Phys Sin, 2012, 61(18):5031-5036.
[18] 刘华明. 多涡卷四阶Jerk系统的仿真研究[J].井冈山大学学报(自然科学版),2013,34(4):59-63. LIU Huaming. Simulation investigation multi-scroll four-order jerk systm[J].Journal of Jinggangshan University(Naturnal Science), 2013, 34(4):59-63.
[19] Podlubny. Fractional differential equation[M]. New York: Academic Press, 1999.
[20] 梅生伟,申铁龙,刘志康.现代鲁棒控制理论与应用[M]. 北京:清华大学出版社,2003.
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