Robust Data-Driven Nash Equilibrium Seeking under Partial-Decision Information

Abstract

This paper presents a data-driven framework for decentralized Nash equilibrium (NE) seeking in multi-agent systems with unknown linear dynamics subject to exogenous disturbances, operating under partial-decision information (where agents lack direct access to the decisions of all others) and equality constraints. The proposed framework integrates an NE model, a distributed communication protocol, an internal model for disturbance rejection, and a data-driven stabilization strategy. By reformulating the problem as a cooperative output regulation problem, we synthesize controllers directly from noisy input-state data via semi-definite programs (SDPs), providing formal guarantees for closed-loop stability and asymptotic convergence to the NE. The approach is further extended to a class of nonlinear systems with constant disturbances by leveraging integral control and describing nonlinearities via quadratic constraints. Numerical simulations involving unmanned aerial vehicle networks and a rotary-wing aerial vehicle formation validate the efficacy and robustness of the proposed method.