Distributed Fixed-Time Nash Equilibrium Seeking via an Estimator-Based Approach

In this paper, a fixed-time algorithm is proposed to solve the Nash equilibrium seeking problem of multi-agent systems in aggregative games. The purpose of this paper is to minimize the cost function of each player. The cost function for each player includes not only the player's own actions but also the sum of all other player actions. We divide the algorithm into two layers: the estimation layer implements the search for Nash equilibrium, while the local control layer implements the tracking of the estimated state. The stability of the two-layer algorithm in fixed-time is proved by the Lyapunov function method. Finally, a simulated example is provided to confirm the algorithm's efficacy.