Distributed robust Nash equilibrium seeking for aggregative games under persistent attacks: A hybrid systems approach

An aggregative game involving double-integrator agents is investigated. In this game, the dynamics of all players are subjected to unknown time-varying disturbances and unmodeled terms, and are also influenced by networked attacks on the communication topology. To seek a Nash equilibrium for such games, a novel distributed robust Nash equilibrium seeking algorithm is proposed and the complete closed-loop system is modeled as a hybrid system using an average dwell-time automaton and a time-ratio monitor to constrain attacks. Then, to analyze stability for the proposed algorithm, a Lyapunov function is constructed and uniform asymptotic stability is obtained under a local Lipschitz assumption on the gradients of the payoff functions. In addition, global uniform asymptotic stability is obtained under a global Lipschitz assumption on the gradients. Finally, an example is used to illustrate the results. (c) 2020 Elsevier Ltd. All rights reserved.