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未知分数阶混沌系统参数辨识问题可转化为函数优化问题, 是实现分数阶混沌系统同步与控制的关键. 结合正交学习机制和原对偶学习策略, 提出一种原对偶状态转移算法, 用于解决分数阶混沌系统的参数辨识问题. 利用正交学习机制产生较优的初始种群增加算法的收敛能力, 并引入原对偶操作增加状态在空间的搜索能力, 提高算法的寻优性能. 在有噪声和无噪声情况下以分数阶多涡卷混沌系统的参数辨识为研究对象进行仿真. 结果表明了该算法的有效性、鲁棒性和通用性.
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关键词:
- 分数阶多涡卷混沌系统 /
- 参数辨识 /
- 原对偶状态转移算法 /
- 正交学习机制
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.-
Keywords:
- fractional-order multi-scroll chaotic systems /
- parameter identification /
- original dual-state transition algorithm /
- orthogonal learning mechanism
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[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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