Riemann-Liouville分数阶P型迭代算法的收敛性  

The convergence analysis of P-type iterative learning control for some Riemann-Liouville fractional system

作　　者：李艳芳 刘向虎 刘衍民 何军 LI Yanfang;LIU Xianghu;LIU Yanmin;HE Jun(School of Mathematics,Zunyi Normal College,Zunyi 563006,China)

机构地区：[1]遵义师范学院数学学院,贵州遵义563006

出　　处：《扬州大学学报（自然科学版）》2018年第4期9-12,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：贵州省教育厅基金资助项目(KY[2015]391);贵州省科技厅资助项目([2016]1160;[2016]1161);贵州省联合基金资助项目(LH[2015]7002);遵义市科合人才基金资助项目([2016]15);遵义师范学院博士基金资助项目(BS[2014]19;BS[2015]09)

摘　　要：运用Laplace变换和Mittag-Leffler函数,研究一类Riemann-Liouville分数阶P型迭代算法的收敛性,建立并证明了开闭环P型迭代算法收敛性定理.结果表明:此算法在Riemann-Liouville分数阶系统中是可行、有效的,拓宽了迭代学习算法的应用范围.Using the Laplace transform and the Mittag-Leffler function,the convergence of iterative learning control for some Riemann-Liouville fractional equation is studied,the sufficient conditions of convergence for the open and closed P-type iterative learning control are obtained.One examples is presented to illustrate the main results.The convergence of the iterative algorithm analysis is studied in the field of fractional order.The result shows that this algorithm is feasible and effective in the Riemann-Liouville fractional order system,and it enriches the theory of iterative algorithm.

关 键 词：Riemann-Liouville分数阶导数 迭代学习控制 收敛性 Mittag-Leffler函数 

分 类 号：O231.2[理学—运筹学与控制论]