Distributed Resilient Nash Equilibrium Seeking Under Network Attacks and Disturbances

This paper investigates the Nash equilibrium (NE) seeking problem of the game in which the dynamics of all players are affected by external disturbances and the communication network among players may be influenced by persistent attacks. To solve this problem, a distributed robust switched algorithm is proposed. This distributed switched strategy consists of two modules: One is the internal-model based dynamics that can be used to compensate the effects caused by external disturbances; the other is gradient-based optimization module which can utilize the local information to estimate the players' decisions and dynamically seek the optimal solution. By utilizing average dwell-time and time-ratio constraints to characterize the network attacks, the proposed switched strategy is modeled into a hybrid dynamical system. Moreover, employing the hybrid systems approach, we prove that the decisions of all players can exponentially converge to the NE of the considered game. Finally, an example is provided to illustrate the theoretical results.