半线性Riemann-Liouville分数阶发展方程反馈时间最优控制  

Time Optimal Control for Semilinear Riemann-Liouville Fractional Evolution Feedback Control Systems

作　　者：宾茂君 施翠云 Bin Maojun;Shi Cuiyun(Center for Applied Mathematics of Guangxi,Yulin Normal University,Guangxi Yulin 537000;Campus of Nanning,Guilin University of Technology,Nanning 530001)

机构地区：[1]广西应用数学中心(玉林师范学院),广西玉林537000 [2]桂林理工大学南宁分校,南宁530001

出　　处：《数学物理学报（A辑）》2024年第3期687-698,共12页Acta Mathematica Scientia

基　　金：广西自然科学基金(2021GXNSFAA220130,2022GXNSFAA035617);广西高校中青年教师科研基础能力提升项目。

摘　　要：该文研究Banach空间中一类半线性Riemann-Liouville.首先,利用不动点定理求解方程的温和解存在唯一性.其次,在半群是紧的前提下借助Cesari性质和Fillipove定理证明容许轨迹集的非空性.在此基础上证明时间反馈最优控制问题的存在性结果.最后,给出实例来说明文章的主要结果.In this article,we investigate a class of time feedback optimal control systems governed by Riemann-Liouville fractional semilinear differential equations in Banach space.At first,we discuss the existence and uniqueness of the mild solution for the equations by using fixed point theorem.Secondly,we show that the admissible trajectories set is nonempty involving the compactness of semigroup T(t)(t>0)with the help of the Cesari roperty and the Fillippove theorem.Moreover,we also give an existence result for time eedback optimal control.In the end,an example is given to illustrate our main results.

关 键 词：半线性分数阶微分方程 容许轨迹 容许控制 反馈控制 时间最优控制 

分 类 号：O175.6[理学—数学]