Distributed Nash equilibrium seeking in multiagent games under switching communication topologies

Abstract

This paper investigates distributed Nash equilibrium seeking in multiagent games under switching communication topologies. To be specific, the communication topology is supposed to be switching among a set of strongly connected digraphs, which might suffer from occasional loss of communication due to sensor failure, packet loss, etc. The synthesis of the leader-following consensus protocol and the gradient play is exploited to achieve the distributed Nash equilibrium seeking under the switching communication topologies. Switching topology without loss of communication is firstly considered, followed by switching topology subject to missing communication within some time slots. For both situations, nonquadratic and quadratic games are addressed separately. Local convergence results are presented for nonquadratic games and nonlocal convergence results are provided for quadratic games. The theoretical results are verified by numerical examples.