Distributed generalized Nash equilibrium seeking: A singular perturbation-based approach

Abstract

In this paper, a distributed optimization algorithm is proposed for aggregative game with coupled constraints. Based on the singular perturbation system, the generalized Nash equilibrium is sought by a group of agents. By employing the average consensus method in the fast manifold, the aggregates in the object function can be estimated via simple information exchanges, as well as the aggregate of dual variables, which provides necessary information for the fully distributed algorithm design. Moreover, the exponential convergence of the proposed algorithm is explored based on the Lyapunov method, the properties of the variational inequality and the characteristic of the singular perturbation system. Application to the resource competition problem in smart grid verifies the effectiveness of the proposed algorithm.