Feedback control for fractional impulsive evolution systems

This paper is mainly concerned with feedback control systems governed by fractional impulsive evolution equations involving Riemann–Liouville derivatives in reflexive Banach spaces. We firstly give an existence and uniqueness result of mild solutions for the equations by applying the Banach’s fixed point theorem. Next, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence result of feasible pairs. We also present an existence result of optimal control pairs for the Lagrange problem.