Controlled Opinion Formation in Multiagent Systems with Constraints on Control Set

We consider a small social network consisting of two agents and one player. The agents’ opinions are influenced by the average social opinion, and the player who also influences the agents’ opinions. The player chooses the set of times to influence only one agent’s opinion, as well as the level of influence to make the society’s opinion as close to his target opinion as possible. The player solves the minimization problem of his costs. In this paper, the player has two options for creating a set of time to control the agent’s opinion: (1) the same time moments are used to monitor the agent’s opinion and control it, and (2) the set of time moments is divided into two subsets, one is for monitoring the agent’s opinion, and another is to use the controls. The linear quadratic optimal control problem is solved using the Euler equation approach. Numerical simulations verify the theoretical results.