Control via Leadership of Opinion Dynamics with State and Time-Dependent Interactions

We study opinion dynamics systems controlled by a leader. Following findings from experimental social psychology, the influence weights considered here have the peculiarity to be both state and time dependent. This allows for instance to model loss of patience or interest of individuals. The opinion of the leader is assumed to be controlled using a saturated control. The objective of the leader is to make all agents agree on a desired consensus value. First, all agents are gathered around the leader, which then steers all agents toward the target consensus value, where consensus is achieved. Trajectory tracking is also investigated. The time-dependent interactions have a significant impact on the control law. To achieve the control, the time-dependent term in the interactions is assumed to be persistent in time. Our results are illustrated by numerical simulation throughout the paper.