Fixed-time consensus-based distributed Nash equilibrium seeking for noncooperative game with second-order players

This paper aims to study the Nash equilibrium (NE) seeking algorithm of noncooperative game with second-order system under strongly connected digraph. In the algorithm, velocity information is not directly accessible to players, in order to avoid the need for additional velocity observers. Meanwhile, for position information, the position estimation of all the other players under local communication is completed in fixed time. To address the aforementioned concern, a NE seeking algorithm with a two-time-scale structure is designed. (1) For reduced system, a second-order velocity estimation model based on state observer is introduced to avoid direct acquisition of velocity information; (2) For fast compensation mechanism, each player uses leader-following consensus protocol to estimate the position of all the other players. The fixed-time consensus protocol is utilized to ensure that the position is estimated in fixed time. Then, aiming to reduce the communication costs and communication burden among players, the event-triggered mechanism is introduced into the above algorithm, and Zeno behavior is excluded. Lastly, a self-organized network problem involving autonomous vehicles is presented to validate the efficacy of the proposed theoretical results.