Distributed Nash Equilibrium Seeking for Games Under Unknown Dead-Zone Inputs and DoS Attacks: A Digital Twin Approach

Abstract

Dear Editor, This letter addresses the Nash equilibrium seeking problem for games with second-order players subject to unknown input dead-zones and denial-of-service (DoS) attacks. By using ideas from the digital twin, a distributed Nash equilibrium seeking strategy is proposed. In the proposed strategy, the twin players are designed to be second-order integrators, based on which a distributed control law is provided so as to find the Nash equilibrium under DoS attacks. Moreover, adaptive control laws and sliding mode control laws are synthesized for the actual players such that they can track the twin players under unknown input dead-zones. Theoretical investigations show that the proposed strategy is effective to drive the actions of actual players to the Nash equilibrium under the given conditions. A numerical example is provided to verify the effectiveness of the proposed strategy.