1 research outputs found
Optimal topology of multi-agent systems with two leaders: a zero-sum game perspective
It is typical to assume that there is no conflict of interest among leaders.
Under such assumption, it is known that, for a multi-agent system with two
leaders, if the followers' interaction subgraph is undirected and connected,
then followers will converge to a convex combination of two leaders' states
with linear consensus protocol. In this paper, we introduce the conflict
between leaders: by choosing k followers to connect with, every leader attempts
all followers converge to himself closer than that of the other. By using graph
theory and matrix theory, we formulate this conflict as a standard two-player
zero-sum game and give some properties about it. It is noteworthy that the
interaction graph here is generated from the conflict between leaders.
Interestingly, we find that to find the optimal topology of the system is
equivalent to solve a Nash equilibrium. Especially for the case of choosing one
connected follower, the necessary and sufficient condition for an interaction
graph to be the optimal one is given. Moreover, if followers' interaction graph
is a circulant graph or a graph with a center node, then the system's optimal
topology is obtained. Simulation examples are provided to validate the
effectiveness of the theoretical results