Prescribed-time distributed Nash equilibrium seeking subject to external disturbances

This paper investigates the problem of Nash equilibrium seeking (NES) for non-cooperative games with external disturbances over multi-agent networks. A two-stage robust Nash equilibrium seeking algorithm is proposed. Two features of this research are worth mentioning. Firstly, the proposed algorithm based on time-varying scaling functions exhibits prescribed-time convergence performance. Secondly, an integral sliding manifold with prescribed-time stability is designed, enabling the proposed algorithm to reject arbitrary disturbances with upper bounds within a prescribed time. Additionally, compared to most existing prescribed-time Nash equilibrium seeking algorithms, this paper also analyzes the boundedness of the proposed input protocol, which is crucial due to the existence of infinite gain resulting from time-varying scaling functions. Finally, a numerical simulation is provided to verify the convergence and disturbance rejection performance of the proposed algorithm.