Constrained Optimal Control of Information Diffusion in Online Social Hypernetworks

With the rapid development of online social networks, issues related to information security and public opinion control have increasingly attracted widespread attention. Therefore, this study establishes a constrained optimal control framework for information diffusion in online social networks, based on the SiSaEIR (Susceptible Inactive–Susceptible Active–Exposed–Informed–Recovered) information diffusion model on social hypernetworks. This framework incorporates both cost and triggering constraints, with the goal of optimally regulating the information diffusion process through dynamic intervention strategies. The existence and uniqueness of the optimal solution are theoretically proven, and the corresponding optimal control strategy is derived. The effectiveness and generality of the model are demonstrated through experiments, and the impact of different combinations of control strategies on system performance enhancement is investigated. The results indicate that the proposed control framework can significantly improve system control effectiveness while satisfying all imposed constraints and exhibits strong generalizability. Not only does this study enrich the theoretical foundation of information diffusion control, but it also provides practical theoretical support for addressing real-world issues such as public opinion guidance and commercial marketing in online social networks.