分数阶系统控制下时间优化问题的可解性  

The solvability for time optimal problems governed by fractional systems

作　　者：练婷婷 李刚[2] LIAN Tingting;LI Gang(Faculty of Mathematics and physics,Yancheng Institute of Technology,Yancheng 224003,China;School of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]盐城工学院数理学院,江苏盐城224003 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2020年第2期5-7,35,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11871064);江苏省高等学校自然科学基金资助项目(18KJB110030).

摘　　要：为了解分数阶微分系统控制下时间优化问题的可解性,利用预解的紧性和一致连续性,结合Schauder不动点定理,得到控制系统适度解的存在性,并通过构造两次时间极小化序列,克服了适度解不唯一的不足,给出了时间优化控制问题的可解性,改进和推广了已有的结果.In order to know the solvability for time optimal problems governed by fractional differential systems,the author derives the existence of mild solutions of control system by using the compactness and unformly continuity of resolvent as well as the Schauder!s fixed point theorem.In addition,the solvability of time optimal control problems is acquired by the new approach of establishing time minimizing sequences twice,which is applied to make up the lack of uniqueness of the mild solution.This work improves and generalizes the results in the existing literature.

关 键 词：分数阶微分系统 时间优化控制 预解 适度解 

分 类 号：O175.15[理学—数学]