Distributed adaptive Nash equilibrium seeking in high-order multiagent systems under time-varying unknown disturbances

This paper aims to tackle two complex challenges in achieving the Nash equilibrium for high-order multiagent systems with unknown disturbances: addressing the interconnection issues arising from the high-order systems, and mitigating the oscillations caused by time-varying unknown disturbances. To address such challenges, we develop a distributed adaptive Nash equilibrium seeking algorithm utilizing a novel state observer comprising the gradient play theory, the leader-following consensus protocol, and the error sign function. This new approach not only achieves the seeking of the Nash equilibrium but also effectively accomplishes the goal of disturbance suppression. The superiority of the proposed strategy over the existing seeking schemes lies in adopting adaptive feedback in the strategy design process. The asymptotic seeking of the Nash equilibrium is then proved by using the input-to-state stability theorem and Barbalat lemma, and sufficient conditions ensuring the convergence are developed. Three simulations consisting of robots with mobile sensor networks, the three-order multiagent system, and the energy competition within power generation systems are conducted to illustrate the effectiveness of the proposed method.