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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (2): 326-340.doi: 10.3969/j.issn.1005-3085.2024.02.009

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分数阶脉冲微分系统的逼近能控性

彭思思   

  1. 深圳市大望学校，深圳 518114
  • 收稿日期:2021-05-28 接受日期:2021-07-30 出版日期:2024-04-15 发布日期:2024-06-15

Approximate Controllability of Fractional Impulsive Differential Systems

PENG Sisi   

  1. Shenzhen Dawang School, Shenzhen 518114
  • Received:2021-05-28 Accepted:2021-07-30 Online:2024-04-15 Published:2024-06-15

摘要： 近年来，脉冲微分系统的能控性引起了人们的重视，这类系统在航天技术、信息科学、控制系统、通讯、生命科学、医学、经济领域均得到重要应用。基于这一原因，在Banach空间中考虑了一类非线性分数阶脉冲微分系统的逼近能控性。目前已有的结果是半线性微分系统中研究，而在脉冲微分系统中研究的，更具有现实意义。首先通过Schauder不动点定理研究了一类非线性分数阶脉冲微分系统温和解的存在性，然后利用半群理论、解算子和预解算子的相关性质，证明这一类系统的逼近能控性，最后给出的实例分析及应用阐明主要结果。

关键词: 分数阶脉冲微分系统, 温和解的存在性, 预解算子, 逼近能控性

Abstract:

In recent years, the controllability of impulsive differential systems has attracted people's attention, and such systems have been applied in aerospace technology, information science, control system, communication, life science, medicine, economy and other fields. For this reason, the approximation controllability of a class of nonlinear fractional order impulsive differential systems is considered in Banach space. Some achievements have been made on the approximation controllability of semilinear differential systems, but the approximation controllability of impulsive differential systems is more practical significance and generalize the existing theoretical results. Firstly, the existence of the fractional impulsive differential systems mild solution is obtained by using Schauder fixed point theorem. Secondly, the approximation controllability of this type of system is studied by applying the semigroup theory and the relevant properties of the solution operators and the resolution operators. Finally, an example analysis and application is given to illustrate the main results.

Key words: fractional impulsive differential systems, existence of mild solution, resolvent operators, approximate controllability

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