Existence of optimal controls for semilinear systems with a nonreflexive control space - Nihale El Boukhari (Statistics, Optimization & Information Computing, 2025)
In this paper, we study the existence of optimal controls that minimize a given functional. We consider a class of infinite-dimensional semilinear systems, and a functional that depends on a control function u and the associated solution of the semilinear equation. The functional is minimized over a set of admissible controls, that is a convex subset of a nonreflexive control space. Under appropriate assumptions, we derive sufficient conditions for the existence of optimal controls, for two classes of semilinear systems. Thereby, we provide two examples of partial differential equations to highlight the obtained results.