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

doi:10.1088/1674-1056/20/12/120506

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120506-120506.doi: 10.1088/1674-1056/20/12/120506

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

陈帝伊, 刘玉晓, 马孝义, 张润凡

Department of Electrical Engineering, College of Water Resources and Architectural Engineering, Northwest Agriculture and Forestry University, Yangling 712100, China

收稿日期:2011-04-18 修回日期:2011-07-27 出版日期:2011-12-15 发布日期:2011-12-15
基金资助:
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).

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

Received:2011-04-18 Revised:2011-07-27 Online:2011-12-15 Published:2011-12-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: fractional-order system, chaos control, sliding mode, uncertain chaotic systems

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

02.30.Uu (Integral transforms) 02.60.Cb (Numerical simulation; solution of equations) 05.45.Pq (Numerical simulations of chaotic systems)

陈帝伊, 刘玉晓, 马孝义, 张润凡. No-chattering sliding mode control in a class of fractional-order chaotic systems[J]. 中国物理B, 2011, 20(12): 120506-120506.

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[J]. Chin. Phys. B, 2011, 20(12): 120506-120506.

参考文献 19

[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

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

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 19

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xiaoming Liang(梁晓明), Chao Fang(方超), Xiyun Zhang(张希昀), and Huaping Lü(吕华平). Influence of coupling asymmetry on signal amplification in a three-node motif[J]. 中国物理B, 2023, 32(1): 10504-010504.
[2]	Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application[J]. 中国物理B, 2022, 31(11): 110501-110501.
[3]	Yun-Xu Ma(马云旭), Jia-Ning Wang(王佳宁), Zhao-Zhuo Zeng(曾钊卓), Ying-Yue Yuan(袁映月), Jin-Xia Yang(杨金霞), Hui-Bo Liu(刘慧博), Sen-Fu Zhang(张森富), Jian-Bo Wang(王建波), Chen-Dong Jin(金晨东), and Qing-Fang Liu(刘青芳). Spin transfer nano-oscillator based on synthetic antiferromagnetic skyrmion pair assisted by perpendicular fixed magnetic field[J]. 中国物理B, 2022, 31(10): 100501-100501.
[4]	Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control[J]. 中国物理B, 2022, 31(10): 100504-100504.
[5]	Tao Li(李涛), Lin Yan(严霖), and Zhigang Zheng(郑志刚). Improved functional-weight approach to oscillatory patterns in excitable networks[J]. 中国物理B, 2022, 31(9): 90502-090502.
[6]	Lei Tao(陶蕾) and Sheng-Jun Wang(王圣军). Power-law statistics of synchronous transition in inhibitory neuronal networks[J]. 中国物理B, 2022, 31(8): 80505-080505.
[7]	Xiang Ling(凌翔), Bo Hua(华博), Ning Guo(郭宁), Kong-Jin Zhu(朱孔金), Jia-Jia Chen(陈佳佳), Chao-Yun Wu(吴超云), and Qing-Yi Hao(郝庆一). Synchronization in multilayer networks through different coupling mechanisms[J]. 中国物理B, 2022, 31(4): 48901-048901.
[8]	Yahan Deng(邓雅瀚), Zhongkai Mo(莫中凯), and Hongqian Lu(陆宏谦). Robust H_∞ state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks[J]. 中国物理B, 2022, 31(2): 20503-020503.
[9]	Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Explosive synchronization: From synthetic to real-world networks[J]. 中国物理B, 2022, 31(2): 20504-020504.
[10]	Alireza Bahramian, Sajjad Shaukat Jamal, Fatemeh Parastesh, Kartikeyan Rajagopal, and Sajad Jafari. Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex[J]. 中国物理B, 2022, 31(2): 28901-028901.
[11]	Dong-Jie Qian(钱冬杰). Explosive synchronization in a mobile network in the presence of a positive feedback mechanism[J]. 中国物理B, 2022, 31(1): 10503-010503.
[12]	Yan-Liang Jin(金彦亮), Run-Zhu Guo(郭润珠), Xiao-Qi Yu(于晓琪), and Li-Quan Shen(沈礼权). Explosive synchronization of multi-layer complex networks based on inter-layer star network connection[J]. 中国物理B, 2021, 30(12): 120505-120505.
[13]	Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay[J]. 中国物理B, 2021, 30(12): 120503-120503.
[14]	Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan. Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control[J]. 中国物理B, 2021, 30(12): 120512-120512.
[15]	Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Adaptive synchronization of chaotic systems with less measurement and actuation[J]. 中国物理B, 2021, 30(10): 100503-100503.