A Double‐Layer Adaptive Nash Equilibrium Seeking Algorithm for Euler‐Lagrange Systems With Parameter Uncertainty

This article investigates the problem of adaptive distributed Nash equilibrium (NE) seeking in non‐cooperative games, where players are modeled as heterogeneous Euler‐Lagrange (EL) systems with parameter uncertainty and cannot access the global information about the algebraic connectivity of the interaction graph. Due to the challenges in algorithm design and analysis arising from these general settings, we develop a novel fully distributed algorithm based on tracking control. A scaling parameter is introduced to adaptively adjust the weights of the edges in the communication graph. To avoid infinite growth of adaptive gains, a damping term is incorporated into the adaptation law for the control gains. By input‐to‐state stability theory, Lyapunov stability theory, and Barbalat's Lemma, it is rigorously proven that the double‐layer adaptive algorithm ensures asymptotic convergence of the system to the NE. Finally, a numerical example in the smart grid electricity markets validates the effectiveness of the algorithm.