分数阶微分算子的最优有理逼近算法  

An Optimal Rational Approximation Algorithm for a Fractional-order Differential Operator

作　　者：潘金文[1] 彭程[1] 王珍[1] 王永[1] 

机构地区：[1]中国科学技术大学自动化系,安徽合肥230026

出　　处：《信息与控制》2014年第5期518-523,共6页Information and Control

基　　金：国家自然科学基金资助项目(60974103;61004017)

摘　　要：在分析经典逼近算法不足的基础上,提出了一种新的分数阶微分算子的实现算法——最优有理逼近算法.推导了最优有理逼近算法的公式,通过数值优化,得出了频带增益的最优轨迹.该算法避免了改进的Oustaloup算法考察频带对称的问题,并具有更高的逼近精度.频域和时域的数值实例验证了使用本算法的优势.Based on the analysis of the shortcomings and deficiencies of classical approximation algorithms, a new approximation scheme is proposed for a fractional-order differential operator - the optimal rational approximation algorithm. We derive the formula of the optimal rational approximation algorithm, and then obtain the optimal trajectory of the band gain by numerical optimization. The proposed algorithm not only avoids the problems caused by the modified Oustaloup algorithm which required that the frequency band of interest should be symmetrical, but also achieves higher precision. The advantages of the proposed algorithm are validated by numerical examples in both the frequency and time domains.

关 键 词：分数阶微积分 分数阶系统 分数阶微分算子 Oustaloup滤波器算法 整数阶近似 最优有理逼近算法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]