Fixed-Time Nash Equilibrium Seeking for Multi-Agent Systems Under External Disturbances

This paper explores the Nash equilibrium seeking within a fixed time in multi-agent systems under external disturbances. To cope with these issues, an algorithm combining the consensus protocol with gradient descent is put forward, which enables the multi-agent system to leverage partial decision information to approximate the Nash equilibrium in non-cooperative games. The first-order algorithm can precisely converge to the Nash equilibrium within a fixed time, with an upper bound that is a constant regardless of the initial state, which can be predefined through proper adjustment of parameters. Numerical simulations were conducted to validate the efficiency of the algorithm that was suggested.