| 一种分数阶微积分算子的有理函数逼近方法 |
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| 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[J].自动化学报,2011,37(8):999-1005. |
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| 作者姓名： | 李文 赵慧敏 |
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| 作者单位： | 1.大连交通大学软件学院 大连 116028 |
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| 基金项目： | 国家自然科学基金(60870009)资助~~ |
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| 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.
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| 关 键 词： | 最佳有理逼近 分数阶微积分算子 有理函数构造 算法验证 |
| 收稿时间： | 2010-7-16 |
| 修稿时间： | 2011-3-22 |
Rational Function Approximation for Fractional Order Differential and Integral Operators |
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| LI Wen,ZHAO Hui-Min.Rational Function Approximation for Fractional Order Differential and Integral Operators[J].Acta Automatica Sinica,2011,37(8):999-1005. |
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| Authors: | LI Wen ZHAO Hui-Min |
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| Affiliation: | 1.Software Institute, Dalian Jiaotong University, Dalian 116028 |
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| Abstract: | A method of constructing the best rational approximation function is proposed based on rational approximation theory for fractional order differential and integral operators in s domain. The idea, method, and algorithm of constructing the best rational approximation function are discussed in detail. The best rational approximation function constructed for fractional integral operator is tested and verified by using best rational approximation definition and characteristic theorem. The verification results show that the proposed method is efficient, and the best rational approximation function constructed can achieve the best approximation performance with the lowest order for a given approximation error and an interested frequency band. |
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| Keywords: | Best rational approximation fractional order differential and integral operators rational function constructing algorithm verification |
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