Results concerning the optimal control for second-order Sobolev-type stochastic integrodifferential equations with impulses and nonlocal conditions

This work explores the optimal control outcomes for second-order Sobolev-type stochastic integrodifferential systems involving impulses and nonlocal conditions. We verify the existence of the mild solutions for the considered system through stochastic analysis and the fixed-point approach involving the cosine family. Additionally, we address the Lagrange problem to confirm the existence of optimal controls. A relevant case study illustrates the key findings of our research.