基于新型趋近律的参数未知分数阶Rucklidge系统的滑模同步

doi:10.6040/j.issn.1672-3961.0.2019.282

山东大学学报 (工学版) ›› 2020, Vol. 50 ›› Issue (4): 40-45.doi: 10.6040/j.issn.1672-3961.0.2019.282

• 控制科学与工程 • 上一篇

基于新型趋近律的参数未知分数阶Rucklidge系统的滑模同步

王春彦¹,邸金红¹,毛北行²

1. 郑州航空工业管理学院智能工程学院, 河南郑州 450015;2. 郑州航空工业管理学院数学学院, 河南郑州 450015

发布日期:2020-08-13
作者简介:王春彦(1979— ),男,河南南阳人,硕士,讲师,主要研究方向为混沌同步.E-mail:wangchunyan555@163.com
基金资助:
国家自然科学基金资助项目(71371173);河南省科技攻关计划资助项目(172102210080)

Sliding mode synchronization of fractional-order Rucklidge systems with unknown parameters based on a new type of reaching law

WANG Chunyan¹, DI Jinhong¹, MAO Beixing²

1. School of Intelligent Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China;
2. College of Mathemtics, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China

Published:2020-08-13

摘要/Abstract

摘要： 利用分数阶微积分理论,基于一种新型趋近律研究不确定分数阶Rucklidge混沌系统的自适应滑模同步问题,根据滑模同步方法给出驱动-响应系统获得滑模混沌同步的充分条件。研究表明:在选取适当的控制器以及滑模函数条件下,驱动-响应系统获得滑模同步,数值仿真表明该方法具有可行性和有效性。

关键词: 分数阶Rucklidge系统, 自适应滑模, 混沌同步, 新型趋近律

Abstract: The problem of self-adaptive sliding mode synchronization of uncertainty fractional-order Rucklidge systems based on a new reaching law was studied with the fractional-order calculus theory. The sufficient conditions were concluded for drive-response systems to get sliding mode chaos synchronization by sliding mode approach. It was proved that drive-response systems were chaos synchronization under proper controllers and sliding mode function. Numerical simulations results verified the feasibility and effectiveness of the proposed method.

Key words: fractional-order Rucklidge systems, self-adaptive sliding mode, chaos synchronization, a new reaching law

中图分类号:

O415.5

王春彦,邸金红,毛北行. 基于新型趋近律的参数未知分数阶Rucklidge系统的滑模同步[J]. 山东大学学报 (工学版), 2020, 50(4): 40-45.

WANG Chunyan, DI Jinhong, MAO Beixing. Sliding mode synchronization of fractional-order Rucklidge systems with unknown parameters based on a new type of reaching law[J]. Journal of Shandong University(Engineering Science), 2020, 50(4): 40-45.

参考文献

[1] 刘雯,常艳娜,赵静一,等.一类三维混沌系统的错位跟踪同步[J].内蒙古农业大学学报(自然科学版),2017,38(1):70-74. LIU Wen, CHANG Yanna, ZHAO Jingyi, et al. Dislocated tracking synchronization of a three dimensional chaotic system[J]. Journal of Inner Mongolia Agricultural University(Natural Science Edition), 2017, 38(1):70-74.
[2] 金世欣,张毅.基于Caputo 分数阶导数的含时滞的非保守系统动力学的Noether对称性[J]. 中山大学学报(自然科学版),2015,54(5):24-31. JIN Shixin, ZHANG Yi. Noether symmetries for non-conservative Lagrange systems with time delay based on Caputo fractional derivative[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2015, 54(5):24-31.
[3] ZHANG Y. Fractional differential equations of motion interms of combined riemann-liouville derivatives[J]. Chinese Physics B, 2012, 8(21): 302-306.
[4] 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.
[5] 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.
[6] 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.
[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] SHAHIRI M, GHADRI R, RANJBAR N, et al. Chaotic fractional-order coullet system: synchronization and control approach[J]. Commun Nonlinear Sci Numer Simul, 2010, 15: 665-674.
[9] HAMAMCI, KOLKSAL M. Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems[J]. Computer Mathematiucs Appllication, 2010, 15: 1267-1278.
[10] MATOUK A. Chaos feedback and synchronization of fractional-order modified autonomous Van der pol-Duffling circuit[J]. Communication Nonlinear Science and Numerical Simulation, 2011, 16: 975-986.
[11] MOHAMMAD P A. Robust finite-time stabilization of fractional-order chaotic susyems based on fractional Lyapunov stability theory[J]. Journal of Computation and Nonlinear Dynamics, 2012, 7: 1011-1015.
[12] MILAD M, HADI D. Synchronization of fractional order hyper-chaotic systems based on a new adaptive sliding mode control[J]. International Journal of Dynamics Control, 2015, 10(7): 435-446.
[13] DELAVARI H, GHADERI R, RANJBAR A, et al. Fuzzy fractional order sliding mode controller for nonlinear systems[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(4): 963-978.
[14] 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(理学版),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(Science Edition), 2016, 54(2):369-373.
[15] DADRAS S,MOMENI H R. Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(1):367-377.
[16] 毛北行,王东晓.分数阶Van der pol振子网络的混沌同步[J].华中师范大学学报(自然科学版),2016,50(2):202-205. MAO Beixing, WANG Dongxiao. Chaos synchronization of fractional-order Van der pol oscillators network systems[J].Journal of Central China Normal University(Natural Science), 2016, 50(2): 202-205.
[17] 周涛.基于一种新型趋近律的自适应滑模控制[J]. 控制与决策,2016,31(7):1335-1338. ZHOU Tao. Adaptive sliding control based on a new reaching law[J]. Control and Decision, 2016, 31(7):1335-1338.
[18] POD L. Fractional differential equation[M]. San Diego, USA: Academic Press, 1999: 715-719.
[19] 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.
[20] 胡建兵,赵灵冬.分数阶系统稳定性理论与控制研究[J].物理学报,2013,62(24):5041-5047. HU Jianbing, ZHAO Lingdong. Research of stability theory of fractional-order systems and control[J]. Acta Phys Sin, 2013, 62(24): 5041-5047.

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基于新型趋近律的参数未知分数阶Rucklidge系统的滑模同步

Sliding mode synchronization of fractional-order Rucklidge systems with unknown parameters based on a new type of reaching law

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