Solvability and Optimal Controls of Impulsive Stochastic Systems in Hilbert Spaces

ABSTRACT This article investigates the solvability and optimal control of a class of impulsive stochastic differential equations (SDEs) within a Hilbert space. Primarily, we justify the existence and uniqueness of mild solutions (MSs) for the proposed impulsive SDE, leveraging fixed‐point theorems and appropriate analytical techniques. Next, we identify and derive the necessary conditions for the existence of optimal control pairs, ensuring the feasibility and effectiveness of the control solutions. Finally, to validate and depict the practical applicability of our theoretical findings, we supply a detailed example showcasing the utility of the results in real‐world scenarios.