An Optimal Feedback Control for Nonautonomous Evolution Equations With Integrodifferential Type

In this paper, we study the optimal feedback control framework for a class of nonautonomous evolution equations involving integrodifferential operators. By leveraging the Cesari property and Filippov’s selection theorem, we first prove the existence of admissible control‐state pairs under relaxed regularity assumptions. Subsequently, we extend these results to establish the existence of optimal control trajectories for a generalized Lagrangian formulation, incorporating nonlocal dynamics and time‐dependent constraints. The analysis emphasizes the interplay between compactness criteria and measurable selection techniques in infinite‐dimensional settings.