带初始状态误差的分数阶P型迭代算法的收敛性分析  

The Convergence Analysis of P-Type Iterative Learning Control with Initial State Error for Some 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 Guizhou 563002, Chin)

机构地区：[1]遵义师范学院数学学院,贵州遵义563006

出　　处：《重庆师范大学学报（自然科学版）》2018年第3期107-112,共6页Journal of Chongqing Normal University:Natural Science

基　　金：遵义师范学院博士基金(No.BS[2014]19;No.BS[2015]09);贵州省联合基金(No.LH[2015]7002);贵州省教育厅基金(No.KY[2015]391;No.KY[2016]046);贵州省教育厅教学改革项目(No.[2015]337);贵州省科技厅项目黔科合基础(No.[2016]1160;No.[2016]1161);遵义市科合人才(No.[2016]15)

摘　　要：【目的】为了解决实际的操作中迭代初态相对于期望初态的误差问题。【方法】通过Laplace变换和M-L函数引导出了弱解的表达式,证明开闭环P型迭代算法收敛的充分条件,最后举例对结果进行验证。【结果】证明了开闭环迭代算法的收敛性。【结论】所得结果拓展了迭代算法在分数阶领域的研究,对已有成果进行了补充。[Purposes]In order to solve the error of the initial state of the iteration compared to the expected initial state in the actual operation. [Methods] According to the Laplace transform and the M-L function,the concept of mild solutions is showed. [Findings] The sufficient conditions of convergence for the open and closed P-type iterative learning control is obtained. Some examples are given to illustrate our main results. [Conclusions] The results extend the research of iterative algorithms in the fractional domain and supplement the existing results.

关 键 词：CAPUTO分数阶导数 迭代学习控制 收敛性 M-L函数 

分 类 号：O29[理学—应用数学]