Synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive neural network control

Lin Fei-Fei; Zeng Zhe-Zhao

doi:10.7498/aps.66.090504

Abstract

Time delay frequently appears in many phenomena of real life and the presence of time delay in a chaotic system leads to its complexity. It is of great practical significance to study the synchronization control of fractional-order chaotic systems with time delay. This is because it is closer to the real life and its dynamical behavior is more complex. However, the chaotic system is usually uncertain or unknown, and may also be affected by external disturbances, which cannot make the ideal model accurately describe the actual system. Moreover, in most of existing researches, they are difficult to realize the synchronization control of fractional-order time delay chaotic systems with unknown terms. In this paper, for the synchronization problems of the different structural fractional-order time delay chaotic systems with completely unknown nonlinear uncertain terms and external disturbances, based on Lyapunov stability theory, an adaptive radial basis function (RBF) neural network controller, which is accompanied by integer-order adaptive laws of parameters, is established. The controller combines RBF neural network and adaptive control technology, the RBF neural network is employed to approximate the unknown nonlinear functions, and the adaptive laws are used to adjust corresponding parameters of the controller. The system stability is analyzed by constructing a quadratic Lyapunov function. This method not only avoids the fractional derivative of the quadratic Lyapunov function, but also ensures that the adaptive laws are integer-order. Based on Barbalat lemma, it is proved that the synchronization error tends to zero asymptotically. In the numerical simulation, the uncertain fractional-order Liu chaotic system with time delay is chosen as the driving system, and the uncertain fractional-order Chen chaotic system with time delay is used as the response system. The simulation results show that the controller can realize the synchronization control of the different structural fractional-order chaotic systems with time delay, and has the advantages of fast response speed, good control effect, and strong anti-interference ability. From the perspective of long-term application, the synchronization of different structures has greater research significance and more development prospect than self synchronization. Therefore, the results of this study have great theoretical significance, and have a great application value in the field of secure communication.

Keywords:

Authors and contacts

1.
College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410076, China

Corresponding author: Zeng Zhe-Zhao, 508984293@qq.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61040049), the Hunan Province Key Discipline of Electronic Science and Technology, and the Foundation of Hunan Province Key Laboratory of Smart Grids Operation and Control, China.

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Cited By

[1]	Hermann R 2010 Physica A 389 4613
[2]	Li C L, Yu S M, Luo X S 2012 Chin. Phys. B 21 100506
[3]	Peterson M R, Nayak C 2014 Phys. Rev. Lett. 113 086401
[4]	Maione G 2013 IEEE Trans. Autom. Control 58 1579
[5]	Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504 (in Chinese) [胡建兵, 赵灵冬 2013 物理学报 62 240504]
[6]	Chen D Y, Zhang R F, Liu X Z, Ma X Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 4105
[7]	Balasubramaniam P, Muthukumar P, Ratnavelu K 2015 Nonlinear Dyn. 80 249
[8]	Muthukumar P, Balasubramaniam P, Ratnavelu K 2015 Nonlinear Dyn. 80 1883
[9]	Gao F, Li T, Tong H Q, Ou Z L 2016 Acta Phys. Sin. 65 230502 (in Chinese) [高飞, 李腾, 童恒庆, 欧卓玲 2016 物理学报 65 230502]
[10]	Andrew L Y T, Li X F, Chu Y D, Zhang H 2015 Chin. Phys. B 24 010502
[11]	Gao Y, Liang C H, Wu Q Q, Yuan H Y 2015 Chaos Soliton. Fract. 76 190
[12]	Khanzadeh A, Pourgholi M 2016 Chaos Soliton. Fract. 91 69
[13]	Maheri M, Arifin N M 2016 Nonlinear Dyn. 85 825
[14]	Chen Y, Li S G, Liu H 2016 Acta Phys. Sin. 65 170501 (in Chinese) [陈晔, 李生刚, 刘恒 2016 物理学报 65 170501]
[15]	Pan G, Wei J 2015 Acta Phys. Sin. 64 040505 (in Chinese) [潘光, 魏静 2015 物理学报 64 040505]
[16]	Wen S F, Shen Y J, Yang S P 2016 Acta Phys. Sin. 65 094502 (in Chinese) [温少芳, 申永军, 杨绍普 2016 物理学报 65 094502]
[17]	Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. B: Cybern. 40 831
[18]	Deng W H, Li C P, L J H 2007 Nonlinear Dyn. 48 409
[19]	Wang Z, Huang X, Shi G D 2011 Comput. Math. Appl. 62 1531
[20]	Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 2178
[21]	Daftardar-Gejji V, Bhalekar S, Gade P 2012 Pramana 79 61
[22]	Liu H R, Yang J 2015 Entropy 17 4202
[23]	Wang S, Yu Y G, Wen G G 2014 Nonlinear Anal. Hybrid Syst. 11 129
[24]	Velmurugan G, Rakkiyappan R 2016 ASME J. Comput. Nonlinear Dyn. 11 031016
[25]	Li D, Zhang X P 2016 Neurocomputing 216 39
[26]	Zeng Z Z 2013 Acta Phys. Sin. 62 030504 (in Chinese) [曾喆昭 2013 物理学报 62 030504]
[27]	Yan X M, Liu D, Guo H J 2010 Control Theory Appl. 27 344 (in Chinese) [阎晓妹, 刘丁, 郭会军 2010 控制理论与应用 27 344]
[28]	Deng L W 2014 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [邓立为 2014 博士学位论文 (哈尔滨: 哈尔滨工业大学)]
[29]	Li C P, Deng W H 2007 Appl. Math. Comput. 187 777
[30]	Tao G 1997 IEEE Trans. Automat. Control 42 698
[31]	Bhalekar S, Daftardar-Gejji V 2011 J. Fract. Calc. Appl. 1 1

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Vol. 66, Issue 9 - 2017-05-05

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