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## 留言板

 引用本文: 李文, 赵慧敏. 一种分数阶微积分算子的有理函数逼近方法. 自动化学报, 2011, 37(8): 999-1005.
LI Wen, ZHAO Hui-Min. Rational Function Approximation for Fractional Order Differential and Integral Operators. ACTA AUTOMATICA SINICA, 2011, 37(8): 999-1005. doi: 10.3724/SP.J.1004.2011.00999
 Citation: LI Wen, ZHAO Hui-Min. Rational Function Approximation for Fractional Order Differential and Integral Operators. ACTA AUTOMATICA SINICA, 2011, 37(8): 999-1005.

## Rational Function Approximation for Fractional Order Differential and Integral Operators

• 摘要: 基于有理函数逼近理论, 提出了一种分数阶微积分算子s域最佳有理逼近函数的构造方法. 详细讨论了构造最佳有理逼近函数的思路、方法及具体算法. 运用最佳有理逼近定义及特征定理, 对所构造的分数阶积分算子最佳有理逼近函数进行了验证. 其结果表明:该分数阶微积分算子最佳有理逼近函数构造方法是有效的, 且对确定的逼近误差及逼近频带, 所构造的最佳有理逼近函数能够以最低阶次取得最佳逼近特性.
•  [1] Gao Chao-Bang, Zhou Ji-Liu. Image enhancement based on quaternion fractional directional differentiation. Acta Automatica Sinica, 2011, 37(2): 150-159(高朝邦, 周激流. 基于四元数分数阶方向微分的图像增强. 自动化学报, 2011, 37(2): 150-159)[2] Li Yuan-Lu, Yu Sheng-Lin. Identification of non-integer order systems in frequency domain. Acta Automatica Sinica, 2007, 33(8): 882-884(李远禄, 于盛林. 非整数阶系统的频域辨识法. 自动化学报, 2007, 33(8): 882-884)[3] Ghanbari M, Haeri M. Order and pole locator estimation in fractional order systems using bode diagram. Signal Processing, 2011, 91(2): 191-202[4] Pu Yi-Fei, Wang Wei-Xing. Fractional differential masks of digital image and their numerical implementation algorithms. Acta Automatica Sinica, 2007, 33(11): 1128-1135(蒲亦非, 王卫星. 数字图像的分数阶微分掩膜及数值运算规则. 自动化学报, 2007, 33(11): 1128-1135)[5] Ozdemir N, Iskender B B. Fractional order control of fractional diffusion systems subject to input hysteresis. Journal of Computational and Nonlinear Dynamics, 2010, 5(2): 1-5[6] Zhao Hui-Min, Li Wen, Deng Wu. Approximation degree selection for one kind of fractional-order filter. Electric Machines and Control, 2010, 14(1): 90-94(赵慧敏, 李文, 邓武. 一类分数阶滤波器逼近阶次的选择. 电机与控制学报, 2010, 14(1): 90-94)[7] Vinagre B M, Podlubny I, Hernandez A, Feliu V. Some approximations of fractional order operators used in control theory and applications. Fractional Calculus and Applied Analysis, 2000, 3(3): 231-248[8] Shaher M, Omar K J, Rabha I. Numerical approximations of a dynamic system containing fractional derivatives. Journal of Applied Sciences, 2008, 8(6): 1079-1084[9] Muslim M, Conca C, Nandakumaran A K. Approximation of solutions to fractional integral equation. Computers and Mathematics with Applications, 2010, 59(3): 1236-1244[10] Hamdaoui K, Charef A. A new discretization method for fractional order differentiators via the bilinear transformation. In: Proceedings of the 15th International Conference on Digital Signal Processing. Cardiff, UK: IEEE, 2007. 280-283[11] Tricaud C, Chen Y Q. An approximate method for numerically solving fractional order optimal control problems of general form. Computers and Mathematics with Applications, 2010, 59(5): 1644-1655[12] Tavakoli-Kakhki M, Haeri M. Model reduction in commensurate fractional-order linear systems. Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering, 2009, 223(4): 493-505[13] Madrid A P D, Manoso C, Hernandez R. New direct discretization of the fractional-order differentiator/integrator by the Chebyshev-Pade approximation. In: Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and Its Applications. Porto, Portugal: Curran Associates, 2006. 166-170[14] Oustaloup A, Levron F, Nanot F, Mathieu B, Nanot F M. Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, 2000, 47(1): 25-39[15] Santouh Z, Charef A, Assabaa M. Approximation of multiple fractional order systems. Arab Research Institute in Sciences and Engineering, 2007, 3(4): 155-161[16] Wang De-Ren, Yang Zhong-Hua. Numerical Approximation Introduction. Beijing: Higher Education Press, 1990. 150-157(王德人, 杨忠华. 数值逼近引论. 北京: 高等教育出版社, 1990. 150-157)[17] Burden R L, Douglas Faires J. Numerical Analysis (Seventh Edition). Belmont: Thomson Learning, 2001. 512-522[18] Li W, Hori Y. Vibration suppression using single neuron-based PI fuzzy controller and fractional-order disturbance observer. IEEE Transactions on Industrial Electronics, 2007, 54(1): 117-126

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##### 出版历程
• 收稿日期:  2010-07-16
• 修回日期:  2011-03-22
• 刊出日期:  2011-08-20

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