Approximate controllability of general impulsive stochastic systems with effects in infinite dimension

In this research, we investigated the feasibility of approximate control for nonlinear impulsive stochastic differential systems defined over infinite-dimensional domains. Our approach is based on the assumption that the associated linear systems are controllable. To this end, we established sufficient conditions to ensure the existence and uniqueness of approximate control solutions for each type of control considered. The theoretical framework is grounded in the application of Banach Fixed Point Theory (BFPT), which serves as a fundamental tool for deriving our results. Furthermore, illustrative examples are provided, incorporating digital media simulations to demonstrate the practical applicability and effectiveness of the proposed method.