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Parameter estimation for fractional-order chaotic systems is a multi-dimensional optimization problem, which is one of the important issues in fractional-order chaotic control and synchronization. With the orthogonal learning strategies and the original dual learning mechanism, the original dual-state transition algorithm is proposed for solving the problem of parameter estimation in fractional-order chaotic systems. The orthogonal learning strategy is presented which can increase the diversity of initial population and improve the convergence ability. And the original dual learning mechanism is presented which can increase the space ability of states, and also can improve the search capability of the algorithm. In the process of identification, we adopt Radau IIA method to solve the fractional-order differential equation. The simulation of the fractional-order multi-scroll chaotic systems with or without noise is conducted and the results demonstrate the e?ectiveness, robustness, and versatility of the proposed algorithm.
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Keywords:
- fractional-order multi-scroll chaotic systems /
- parameter identification /
- original dual-state transition algorithm /
- orthogonal learning mechanism
[1] Zhao Y B, Zhang X Z, Sun X Y 2014 Acta Phys. Sin. 63 130503 (in Chinese) [赵益波, 张秀再, 孙心宇 2014 63 130503]
[2] Wang S E, Wang W W, Liu F C, Tang Y G, Guan X P 2015 Nonlinear Dynam. 81 1081
[3] Zhang H L, Song L L 2013 Acta Phys. Sin 62 190508 (in Chinese) [张宏立, 宋莉莉 2013 62 190508]
[4] Hu W, Yu Y G 2015 Nonlinear Dynam. 82 1441
[5] Lin J 2014 Nonlinear Dynam. 77 983
[6] Li X, Yin M 2014 Nonlinear Dynam. 77 61
[7] Li C S, Zhou J Z, Xiao J, Xiao H 2012 Chaos Solit. Fract. 45 539
[8] Huang Y, Liu Y F, Peng Z M 2015 Acta Phys. Sin. 64 030305 (in Chinese) [黄宇, 刘玉峰, 彭志敏 2015 64 030505]
[9] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 305
[10] Zhou X J, Yang C H, Gui W H 2011 The 2th International Conference on Digital Manufacturing and Automation (ICDMA)Zhangjiajie, China, Dec. 9, 2011 p644
[11] Zhou X J, Yang C H, Gui W H 2011 The 2th International Conference on Intelligent Control and Information Processing Harbin, China, August 1, 2011 p674
[12] Li X T, Yin M H 2012 Chin. Phys. B 21 050507
[13] Gong W Y, Cai Z H, Jiang L X 2008 Applied Mathematics and Computation 56 206
[14] Le Y W, Wang Y 2001 IEEE Trans. Evolut. Comput. 5 41
[15] Tai J T, Liu T K, Chou J H 2004 IEEE Trans. Evolut. Comput. 8 365
[16] Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi An: Xian University of Electronic Science and Technology press) pp316-323 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第 316-323 页]
[17] Wang H Y 2008 M. S. Dissertation (Xiangtan: Xiangtan University) (in Chinese) [王海燕 2008 硕士学位论文 (湘潭: 湘潭大学)]
[18] Igor P 1999 Fractional Differential Equations (San Diego: Academic press)p124
[19] Sprott J C 2000 Amer. J. Phys. 68 758
[20] Sprott J C 2000 Phys. Lett. A 266 19
[21] Ahmad W M, Sprott J C 2003 Chaos Solit. Fract. 16 339
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[1] Zhao Y B, Zhang X Z, Sun X Y 2014 Acta Phys. Sin. 63 130503 (in Chinese) [赵益波, 张秀再, 孙心宇 2014 63 130503]
[2] Wang S E, Wang W W, Liu F C, Tang Y G, Guan X P 2015 Nonlinear Dynam. 81 1081
[3] Zhang H L, Song L L 2013 Acta Phys. Sin 62 190508 (in Chinese) [张宏立, 宋莉莉 2013 62 190508]
[4] Hu W, Yu Y G 2015 Nonlinear Dynam. 82 1441
[5] Lin J 2014 Nonlinear Dynam. 77 983
[6] Li X, Yin M 2014 Nonlinear Dynam. 77 61
[7] Li C S, Zhou J Z, Xiao J, Xiao H 2012 Chaos Solit. Fract. 45 539
[8] Huang Y, Liu Y F, Peng Z M 2015 Acta Phys. Sin. 64 030305 (in Chinese) [黄宇, 刘玉峰, 彭志敏 2015 64 030505]
[9] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 305
[10] Zhou X J, Yang C H, Gui W H 2011 The 2th International Conference on Digital Manufacturing and Automation (ICDMA)Zhangjiajie, China, Dec. 9, 2011 p644
[11] Zhou X J, Yang C H, Gui W H 2011 The 2th International Conference on Intelligent Control and Information Processing Harbin, China, August 1, 2011 p674
[12] Li X T, Yin M H 2012 Chin. Phys. B 21 050507
[13] Gong W Y, Cai Z H, Jiang L X 2008 Applied Mathematics and Computation 56 206
[14] Le Y W, Wang Y 2001 IEEE Trans. Evolut. Comput. 5 41
[15] Tai J T, Liu T K, Chou J H 2004 IEEE Trans. Evolut. Comput. 8 365
[16] Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi An: Xian University of Electronic Science and Technology press) pp316-323 (in Chinese) [禹思敏 2011 混沌系统与混沌电路 (西安: 西安电子科技大学出版社) 第 316-323 页]
[17] Wang H Y 2008 M. S. Dissertation (Xiangtan: Xiangtan University) (in Chinese) [王海燕 2008 硕士学位论文 (湘潭: 湘潭大学)]
[18] Igor P 1999 Fractional Differential Equations (San Diego: Academic press)p124
[19] Sprott J C 2000 Amer. J. Phys. 68 758
[20] Sprott J C 2000 Phys. Lett. A 266 19
[21] Ahmad W M, Sprott J C 2003 Chaos Solit. Fract. 16 339
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