| 一类分数阶微分方程的最优控制 |
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| 引用本文： | 司家芳,蒋威. 一类分数阶微分方程的最优控制[J]. 生物数学学报, 2011, 0(1): 17-24 |
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| 作者姓名： | 司家芳 蒋威 |
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| 作者单位： | 安徽大学数学科学学院,安徽合肥230039 |
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| 基金项目： | Supported by the National Nature Science Foundation of China（No.11071001）; The Special Research Fund for the Doctoral Program of the Ministry of Education of China（20093401110001）; Major Programs of Natural Science Research in Anhui Universities（KJ2010ZD02） |
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| 摘 要： | 主要研究了一类分数阶微分方程的最优控制问题.通过Oustaloup迭代逼近,可以将分数阶微分算子在频率域范围内进行近似.那么原先的分数阶微分方程就转换为一般的常微分方程.利用这个关系,可以得到关于分数阶微分方程的两个定理和一个引理.最后给出一个例子说明该方法的有效性.
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| 关 键 词： | 分数阶微分方程 Laplace变换 最优控制 |
The Optimal Control for a Class of Fractional Differential Equations |
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| SI Jia-Fang JIANG Wei. The Optimal Control for a Class of Fractional Differential Equations[J]. Journal of Biomathematics, 2011, 0(1): 17-24 |
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| Authors: | SI Jia-Fang JIANG Wei |
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| Affiliation: | SI Jia-Fang JIANG Wei (School of Mathematical Science,Anhui University,Hefei Anhui 230039 China) |
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| Abstract: | This paper studies the optimal control for a class of fractional differential equations（FDEs）.By using Oustaloup＇s Recursive Approximation,the fractional derivative operator can be approximated in frequency-domain.Then the original FDE is reformulated to an ordinary differential equation（ODE）.Using this relation,two theorems and a lemma on optimal control of FDEs are obtained.Finally,a illustrative example is given. |
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| Keywords: | Fractional differential equations Laplace transformation Optimal control |
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