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

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.