Optimal feedback control for a class of fractional evolution equations with history-dependent operators

In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators. Then, by introducing a feedback iterative technique and applying Filippov theorem, we show the existence of feasible pairs and optimal control pairs of the optimal feedback control systems with history-dependent operators. Finally, we give some applications to illustrate our main results.

Automated summary

This paper investigates optimal feedback control problems derived from a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. The existence and uniqueness of mild solutions are proved, feasible pairs and optimal control pairs are demonstrated to exist for optimal feedback control systems with history-dependent operators using a feedback iterative technique and Filippov theorem, and some applications are provided to illustrate the main results.