Abstract
This paper studies the optimal consensus control of linear multi-agent systems with deceptive agents or traitorous agents. An error-effort ratio is defined to quantify an agent's income in the communication decision process and a false information counter-attack mechanism is proposed to reduce the deceptive agent's income from transmitting false information and enforce the transmission of true state information. Moreover, a traitor removal strategy is proposed to identify traitors camouflaging themselves as friendly agents, followed by the traitor removal algorithm to reset the edge weights of communication topology to eliminate traitors. Each agent hopes to minimize its own cost in achieving consensus, forming a differential game. With the proposed algorithm, the control strategies of friendly agents and deceptive agents can reach a Nash equilibrium of the differential game and enable non-traitors to achieve consensus under the interference of traitors. As illustrative examples, the game solution is applied to the distributed voltage control problem in AC microgrids and the formation tracking control problem of a quad-rotor uncrewed aerial vehicle swarm.