Time optimal control for semilinear fractional evolution feedback control systems

In this article, we investigate a class of time feedback optimal control systems governed by Caputo 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 non-empty involving the compactness of semigroup T(t)(t>0) with the help of the Cesari property and the Fillippove theorem. Moreover, we also give an existence result for time feedback optimal control. In the end, an example is given to illustrate our main results.