The convergence of iterative learning control for some fractional system

Advances in Difference Equations

Yanfang Li¹  Yanmin Liu¹  Xianghu Liu² 

[1] Mathematics Department, Zunyi Normal College, Zunyi, P.R. China;School of Mathematics and Computer Science, Guizhou University, Guiyang, P.R. China

关键词: Caputo fractional derivative;    iterative learning control;    convergence;    Gronwall ineqality;    P-type;    Mittag-Leffler function;    93C10;    93C40;   

DOI  :  10.1186/s13662-017-1177-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the convergence of iterative learning control for some fractional equation. Firstly, by using the Laplace transform and the M-L function, we show the concept of mild solutions. Secondly, by using the Gronwall inequality, we show the sufficient conditions of convergence for the open P-type and the close P-type iterative learning control. At last, we give some examples to illustrate our main results.

【 授权许可】

CC BY