您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(工学版)》

山东大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (3): 79-83.doi: 10.6040/j.issn.1672-3961.0.2016.058

• • 上一篇    下一篇

分数阶多涡卷系统滑模控制混沌同步

毛北行,王东晓   

  1. 郑州航空工业管理学院理学院, 河南 郑州 450015
  • 收稿日期:2016-02-18 出版日期:2017-06-20 发布日期:2016-02-18
  • 作者简介:毛北行(1976— ),男,河南洛阳人,副教授,理学硕士,主要研究方向为复杂网络与混沌同步.E-mail:bxmao329@163.com
  • 基金资助:
    国家自然科学青年基金资助项目(NSFC11501525);河南省科技厅软科学资助项目(142400411192);河南省高等学校青年骨干教师资助计划资助项目(2013GGJS-142);河南省高等学校重点科研资助项目(15B110011)

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

摘要: 基于分数阶微积分理论以及滑膜控制研究方法,研究具有确定参数和不确定参数两种情形下分数阶多涡卷系统的滑模混沌同步问题。给出两种情形下切换函数的构造,设计出控制器,并给出系统取得同步的两个充分性条件。研究结果表明:在适当的选取控制律以及自适应控制律下,多涡卷误差系统取得滑模混沌同步。

关键词: 分数阶, 滑模, 混沌同步, 多涡卷系统

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

中图分类号: 

  • 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.
[1] 王东晓. 具有纠缠项的分数阶五维混沌系统滑模同步的两种方法[J]. 山东大学学报(工学版), 2018, 48(5): 85-90.
[2] 王春彦,邸金红. 基于降阶方法的分数阶多涡卷混沌系统的同步控制[J]. 山东大学学报(工学版), 2018, 48(5): 91-94.
[3] 孟晓玲,王建军. 一类分数阶冠状动脉系统的混沌同步控制[J]. 山东大学学报(工学版), 2018, 48(4): 55-60.
[4] 毛北行. 纠缠混沌系统的比例积分滑模同步[J]. 山东大学学报(工学版), 2018, 48(4): 50-54.
[5] 李翔宇,赵志诚,王文逾. 基于反向解耦的PWM整流器分数阶内模控制[J]. 山东大学学报(工学版), 2018, 48(4): 109-115.
[6] 谢晓龙,姜斌,刘剑慰,蒋银行. 基于滑模观测器的异步电动机速度传感器故障诊断及容错控制[J]. 山东大学学报(工学版), 2017, 47(5): 210-214.
[7] 毛北行,程春蕊. 分数阶Victor-Carmen混沌系统的自适应滑模控制[J]. 山东大学学报(工学版), 2017, 47(4): 31-36.
[8] 李庆宾,王晓东. 分数阶情绪模型的终端滑模控制混沌同步[J]. 山东大学学报(工学版), 2017, 47(3): 84-88.
[9] 梁秋实,赵志诚. 基于分数阶滑模观测器的BLDCM无位置传感器控制[J]. 山东大学学报(工学版), 2017, 47(3): 96-101.
[10] 唐庆顺,金璐,李国栋,吴春富. 基于自适应终端滑模控制器的机械手跟踪控制[J]. 山东大学学报(工学版), 2016, 46(5): 45-53.
[11] 刘向杰,韩耀振. 基于连续高阶模滑的多机电力系统励磁控制[J]. 山东大学学报(工学版), 2016, 46(2): 64-71.
[12] 赵以阁, 王玉振. 分数阶非线性三角系统的状态反馈控制器设计[J]. 山东大学学报(工学版), 2015, 45(6): 29-35.
[13] 孙美美, 胡云安, 韦建明. 多涡卷超混沌系统自适应滑模同步控制[J]. 山东大学学报(工学版), 2015, 45(6): 45-51.
[14] 赵志涛, 赵志诚, 王惠芳. 直流调速系统模糊自整定分数阶内模控制[J]. 山东大学学报(工学版), 2015, 45(5): 58-62.
[15] 王惠芳, 赵志诚, 张井岗. 一种高阶系统的分数阶IMC-IDμ控制器设计[J]. 山东大学学报(工学版), 2014, 44(6): 77-82.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!