Robust distributed Nash equilibrium seeking via data-driven output regulation

This paper resolves the problem of distributed Nash equilibrium (NE) seeking for network games on weakly connected graphs involving linear or nonlinear players subject to external disturbances. Unlike existing approaches, we assume that the dynamics of the players are unknown and characterize them using input-state data collected a priori. The NE seeking problem is reformulated as a data-driven cooperative output regulation problem. For linear players, we develop a data-driven internal model-based approach that leverages local and neighboring output measurements to achieve NE while ensuring stability through the solution of a linear matrix inequality. This framework is extended to nonlinear players affected by constant disturbances, where vector fields are represented using a dictionary of basis functions. The proposed solution employs integral control and semi-definite programming techniques. Numerical simulations, including applications to mobile robots and single-link manipulators, demonstrate the efficacy and practicality of the proposed methods.