Fully distributed edge-based adaptive Nash equilibrium seeking with input constraints

The present study investigates the quest for a fully distributed Nash equilibrium (NE) in networked non-cooperative games, with particular emphasis on actuator limitations. Existing distributed NE seeking approaches often overlook practical input constraints or rely on centralized information. To address these issues, a novel edge-based double-layer adaptive control framework is proposed. Specifically, adaptive scaling parameters are embedded into the edge weights of the communication graph, enabling a fully distributed scheme that avoids dependence on centralized or global knowledge. Every participant modifies its strategy by exclusively utilizing local information and communicating with its neighbors to iteratively approach the NE. By incorporating damping terms into the design of the adaptive parameters, the proposed approach effectively suppresses unbounded parameter growth and consequently guarantees the boundedness of the adaptive gains. In addition, to account for actuator saturation, the proposed distributed NE seeking approach incorporates a saturation function, which ensures that control inputs do not exceed allowable ranges. A rigorous Lyapunov-based analysis guarantees the convergence and boundedness of all system variables. Finally, the presentation of simulation results aims to validate the efficacy and theoretical soundness of the proposed approach.