Two-period optimal control for opinion dynamics

This paper considers an optimal control problem in opinion dynamics, where the time interval is assumed to be divided into two segments. In one segment, the agent is under the player's control, while in the other, the player does not exert control. The goal of the player is to bring the agent's opinion close to a specific target value, while the player aims to minimize the payment function. By solving the player's closed-loop optimal control using the HJB equation method and applying the Pontryagin Maximum Principle to derive the player's open-loop optimal control, the simulation results indicate that the player incurs higher costs when implementing closed-loop control.