Opinion dynamics control by leadership with bounded influence

In the present paper, we provide results on the control of general opinion dynamics systems. The control is applied to one agent only, called the leader. Explicit control laws ensure three complementary desired behaviours of the system: i) drag all agents arbitrarily close to the leader, then ii) make all agents follow the leader toward a targeted value, iii) make all agents converge to a targeted consensus value. Unlike the existing literature, the control is carried out under weak assumptions on the leader influence. In particular, the leader may only have a bounded influence range (this for instance includes the Hegselmann-Krause bounded confidence model). Finally our results are illustrated by numerical examples.