Foraging motion of swarms with leaders as Nash equilibria. (November 2016)

• Record Type: Journal Article
• Authors: Yıldız, Aykut; Özgüler, A. Bülent
• Is Part Of: Automatica. Volume 73(2016)
• Page Start: 163
• Page End: 168
• Publication Date: 2016-11
• Subjects: Leader–follower -- Rendezvous problem -- Ordered graph -- Directed star -- Nash equilibrium -- Swarm -- Foraging -- Multi-agent systems -- Differential game theory; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.07.024
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The consequences of having a leader in a swarm are investigated using differential game theory. We model foraging swarms with leader and followers as a non-cooperative, multi-agent differential game. The agents in the game start from a set of initial positions and migrate towards a target. The agents are assumed to have no desire, partial desire or full desire to reach the target. We consider two types of leadership structures, namely hierarchical leadership and a single leader. In both games, the type of leadership is assumed to be passive. We identify the realistic assumptions under which a unique Nash equilibrium exists in each game and derive the properties of the Nash solutions in detail. It is shown that having a passive leader economizes in the total information exchange at the expense of aggregation stability in a swarm. It turns out that, the leader is able to organize the non-identical followers into harmony under missing information.