Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(12): 120506    DOI: 10.1088/1674-1056/20/12/120506
GENERAL Prev   Next  

No-chattering sliding mode control in a class of fractional-order chaotic systems

Chen Di-Yi(陈帝伊), Liu Yu-Xiao(刘玉晓), Ma Xiao-Yi(马孝义), and Zhang Run-Fan(张润凡)
Department of Electrical Engineering, College of Water Resources and Architectural Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China
Abstract  A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
Keywords:  fractional-order system      chaos control      sliding mode      uncertain chaotic systems  
Received:  18 April 2011      Revised:  27 July 2011      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  02.30.Uu (Integral transforms)  
  02.60.Cb (Numerical simulation; solution of equations)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 51109180) and the Personal Special Fund of Northwest Agriculture and Forestry University, China (Grant No. RCZX-2009-01).

Cite this article: 

Chen Di-Yi(陈帝伊), Liu Yu-Xiao(刘玉晓), Ma Xiao-Yi(马孝义), and Zhang Run-Fan(张润凡) No-chattering sliding mode control in a class of fractional-order chaotic systems 2011 Chin. Phys. B 20 120506

[1] Gao X and Yu J B 2005 emphChin. Phys. 14 908
[2] Wang X Y, He Y J and Wang M J 2009 emphNonlinear Analysis: Theory, Methods and Applications 71 6126
[3] Jia L X, Dai H and Hui M 2010 emphChin. Phys. B 19 110509
[4] Zhou P and Kuang F 2010 emphActa Phys. Sin. 59 6851 (in Chinese)
[5] Su X W 2011 emphNonlinear Analysis: Theory, Methods and Applications 74 2844
[6] Zheng Y G, Nian Y B and Wang D J 2010 emphPhys. Lett. A 375 125
[7] Matouk A E 2011 emphCommun. Nonlinear Sci. Numer. Simul. 16 975
[8] Zhou S B, Lin X R and Li H 2011 emphCommun. Nonlinear Sci. Numeri. Simul. 16 1533
[9] Wang J W and Chen A M 2010 emphChin. Phys. Lett. 27 110501
[10] Zhou P, Cheng Y M and Kuang F 2010 emphChin. Phys. B 19 090503
[11] Zhang R X and Yang S P 2009 emphChin. Phys. B 18 3295
[12] Liu F C, Li J Y and Zang X F 2011 emphActa Phys. Sin. 60 108 (in Chinese)
[13] Zhao L D, Hu J B and Liu X H 2010 emphActa Phys. Sin. 59 2305 (in Chinese)
[14] Wang X Y, Zhang Y L, Lin D and Zhang N 2011 emphChin. Phys. B 20 030506
[15] Chen D Y, Liu Y X, Ma X Y and Zhang R F 2011 emphNonlinear Dyn. DOI: 10.1007/s11071-011-0002-x
[16] Sheu L J, Chen H K, Chen J H and Tam L M 2007 emphChaos, Solitons and Fractals 31 1203
[17] Peng G J and Jiang Y L 2010 emphPhysica A 389 4140
[18] Song L, Yang J Y and Xu S Y 2010 emphNonlinear Analysis 72 2326
[19] Sara D and Momeni H R 2010 emphPhysica A 389 2434
[1] Control of chaos in Frenkel-Kontorova model using reinforcement learning
You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[2] Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system
Fei Gao(高飞), Wen-Qin Li(李文琴), Heng-Qing Tong(童恒庆), Xi-Ling Li(李喜玲). Chin. Phys. B, 2019, 28(9): 090501.
[3] Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system
Jiang-Bin Wang(王江彬), Chong-Xin Liu(刘崇新), Yan Wang(王琰), Guang-Chao Zheng(郑广超). Chin. Phys. B, 2018, 27(7): 070503.
[4] A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control
Jay Prakash Singh, Binoy Krishna Roy, Zhouchao Wei(魏周超). Chin. Phys. B, 2018, 27(4): 040503.
[5] Coordinated chaos control of urban expressway based on synchronization of complex networks
Ming-bao Pang(庞明宝), Yu-man Huang(黄玉满). Chin. Phys. B, 2018, 27(11): 118902.
[6] Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control
Yangui Xi(喜彦贵), Yongguang Yu(于永光), Shuo Zhang(张硕), Xudong Hai(海旭东). Chin. Phys. B, 2018, 27(1): 010202.
[7] Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system
Ningning Yang(杨宁宁), Yuchao Han(韩宇超), Chaojun Wu(吴朝俊), Rong Jia(贾嵘), Chongxin Liu(刘崇新). Chin. Phys. B, 2017, 26(8): 080503.
[8] Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control
Xiang Zhang(张翔), Jin-Huan Wang(王金环), De-Dong Yang(杨德东), Yong Xu(徐勇). Chin. Phys. B, 2017, 26(7): 070501.
[9] Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme
Alireza Khanzadeh, Mahdi Pourgholi. Chin. Phys. B, 2016, 25(8): 080501.
[10] Controlling chaos based on a novel intelligent integral terminal sliding mode control in a rod-type plasma torch
Safa Khari, Zahra Rahmani, Behrooz Rezaie. Chin. Phys. B, 2016, 25(5): 050201.
[11] Parrondo's paradox for chaos control and anticontrol of fractional-order systems
Marius-F Danca, Wallace K S Tang. Chin. Phys. B, 2016, 25(1): 010505.
[12] Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization
Donato Cafagna, Giuseppe Grassi. Chin. Phys. B, 2015, 24(8): 080502.
[13] Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance
Zhou Ke (周柯), Wang Zhi-Hui (王智慧), Gao Li-Ke (高立克), Sun Yue (孙跃), Ma Tie-Dong (马铁东). Chin. Phys. B, 2015, 24(3): 030504.
[14] Full-order sliding mode control of uncertain chaos in a permanent magnet synchronous motor based on a fuzzy extended state observer
Chen Qiang (陈强), Nan Yu-Rong (南余荣), Zheng Heng-Huo (郑恒火), Ren Xue-Mei (任雪梅). Chin. Phys. B, 2015, 24(11): 110504.
[15] Control of fractional chaotic and hyperchaotic systems based on a fractional order controller
Li Tian-Zeng (李天增), Wang Yu (王瑜), Luo Mao-Kang (罗懋康). Chin. Phys. B, 2014, 23(8): 080501.
No Suggested Reading articles found!