JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2017, Vol. 47 ›› Issue (4): 31-36.doi: 10.6040/j.issn.1672-3961.0.2016.327

Previous Articles     Next Articles

Self-adaptive sliding mode control of fractional-order Victor-Carmen chaotic systems

MAO Beixing, CHENG Chunrui   

  1. College of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, Henan, China
  • Received:2016-10-18 Online:2017-08-20 Published:2016-10-18

PDF (PC)

340

Abstract: The problem of sliding mode synchronization of fractional-order Victor-Carmen systems was studied using self-adaptive sliding mode control approach based on fractional-order calculus theory. The fractional-order slding mode function was designed, the controllers and the strict proof in mathematics using Lyapunov stability theory were given. Two sufficient conditions were arrived for the fractional order systems getting sliding model synchronization. The research conclusion illustrated that fractional-order multi-scroll systems was sliding mode chaos synchronization under proper controllers and sliding mode surface.The numerical simulations demonsrrated the effectiveness of the proposed method.

Key words: fractional-order, Victor-Carmen systems, chaos synchronization, sliding mode

CLC Number: 

  • O482.4
[1] 丁金凤,张毅. 基于按指数律拓展的分数阶积分的El-Nabulsi-Pfaff 变分问题的Noether 对称性[J].中山大学学报(自然科学版), 2014, 54(6):150-154. DING Jinfeng, ZHANG Yi.Neother symmetries for El-Nabulsi-Pfaff variational problem for extended exponential fractional integral[J]. Journal of Zhongshan University(Science Edition), 2014, 53(6):150-154.
[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):49-55. JIN Shixin, ZHANG Yi. Noether symmetries for non-conservative Lagrange systems with time delay based on Caputo fractional derivative[J]. Journal of Zhongshan University(Science Edition), 2015, 54(5):49-55.
[3] ZHANG Yi. 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] 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 Jiling University(Science Edition), 2015, 53(4):757-761.
[9] 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, 32(7):1011-1015.
[10] MILAD Mohadeszadeh, HADI Delavari.Synchronization of fractional order hyper-chaotic systems based on a new adaptive sliding mode control[J].International Journal of Dynamics and Control, 2015, 10(7):435-446.
[11] WANG X, HE Y.Projective synchronization of fractional order chaotic system based on linear separation[J].Phys Lett A, 2008, 37(12):435-441.
[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), 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 mede adaptive synchronization for a class of fractional-order chaotic 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, 2012, 17(2):46-49.
[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] GRIGORAS V, GRIGORAS C. A novel chaotic systems for random pulse generation[J].Advanced in Electrical and Computer Engineering, 2014, 14(2):109-112.
[17] 徐瑞萍, 高明美. 自适应终端滑模控制不确定混沌系统的同步[J].控制工程, 2016, 23(5):715-719. XU Ruiping, GAO Mingmei. Synchronization of chaotic susyems with uncertainty using adaptive terminal sliding mode controller[J].Control Engineering of China, 2016, 23(5):715-719.
[18] PODLUBN Y. Fractional differential equation[M]. New York:Academic Press, 1999.
[19] BHAT S P, BERNSTEIN D S. Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control Signals and Systems, 2005, 17(2):101-127.
[20] MOHAMMAD P A, SOHRAB K, GHASSE Mhassem A. Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique[J]. Applied Mathematical Modelling, 2011, 35(6):3080-3091.
[1] WANG Dongxiao. Two methods for sliding mode synchronization of five-dimensional fractional-order chaotic systems with entanglement iterms [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(5): 85-90.
[2] WANG Chunyan, DI Jinhong. Synchronization control of fractional-order multi-scroll chaotic system based on reduced-order method [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(5): 91-94.
[3] MAO Beixing. Ratio integral sliding mode synchronization control of entanglement chaotic systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(4): 50-54.
[4] MENG Xiaoling, WANG Jianjun. Chaos synchronization of a class of fractional-order coronary artery systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(4): 55-60.
[5] LI Qingbin, WANG Xiaodong. Terminal sliding model control chaos synchronization of fractional-order emotion mode systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 84-88.
[6] MAO Beixing, WANG Dongxiao. Sliding model chaos synchronization control of a class of fractional-order multi-scroll systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 79-83.
[7] LIANG Qiushi, ZHAO Zhicheng. A position sensorless control strategy for BLDCM based on a fractional order sliding mode observer [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 96-101.
[8] TANG Qingshun, JIN Lu, LI Guodong, WU Chunfu. Robotic manipulators tracking control based on adaptive terminal sliding mode controller [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(5): 45-53.
[9] LIU Xiangjie, HAN Yaozhen. Multi-machine power system excitation control based on continuous higher-order sliding mode [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(2): 64-71.
[10] SUN Meimei, HU Yun'an, WEI Jianming. Synchronization of multiwing hyperchaotic systems via adaptive sliding mode control [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2015, 45(6): 45-51.
[11] XIE Jing, KAO Yonggui, GAO Cunchen, ZHANG Mengqiao. Integral sliding mode control for uncertain stochastic singular Markovian jump systems with time-varying delays [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2014, 44(4): 31-38.
[12] ZHAO Zhan-shan1,2, ZHANG Jing3, SUN Lian-kun, DING Gang1. Design of self-adaptive sliding mode controller with finite time convergence [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2012, 42(4): 74-78.
[13] JIN Xin,JIANG Ming-yan . Chaos synchronization control for a new chaotic system with diverse structures base on nonlinear control [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2007, 37(5): 78-82 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of Journal of Shandong University (Engineering Science)
Supported by Beijing Magtech Co.Ltd