Solvability and Optimal Controls of Impulsive Stochastic Evolution Equations in Hilbert Spaces

Abstract

This paper investigates the solvability and optimal control of a class of impulsive stochastic differential equations (SDEs) within a Hilbert space setting. First, we establish the existence and uniqueness of mild solutions for the proposed impulsive stochastic system, 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 demonstrate the practical applicability of our theoretical findings, we provide a detailed example showcasing the utility of the results in real-world scenarios.

arXiv commentOptimal Control Applications and Methods (2025)

References in corpus (3)

• Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces
• Approximate controllability of impulsive semilinear evolution equations in Hilbert spaces
• Remarks on finite-approximate controllability of impulsive evolution systems via resolvent-like operator in Hilbert spaces