  A closed-loop control model to analyze the impact of recommendation systems
on opinion dynamics within social networks is introduced. The core contribution
is the development and formalization of model-free and model-based approaches
to recommendation system design, integrating the dynamics of social
interactions within networks via an extension of the Friedkin-Johnsen (FJ)
model. Comparative analysis and numerical simulations demonstrate the
effectiveness of the proposed control strategies in maximizing user engagement
and their potential for influencing opinion formation processes.
