Continuous-Time Distributed Generalized Nash Equilibrium Seeking in Nonsmooth Fuzzy Aggregative Games

Jingxin Liu, Xiaofeng Liao, Jin Song Dong, Amin Mansoori

Abstract: This article explores the variational generalized Nash equilibrium seeking for a class of fuzzy aggregative games, where each player's cost function is fuzzy and nonsmooth, and the strategy profile is constrained by a coupling nonlinear inequality, a affine coupling equality with $\alpha$-cuts and heterogeneous local convex sets. Under the differential inclusion framework, a continuous-time distributed algorithm with a derivative feedback term is proposed. Benefiting from this algorithm, each player is assigned several auxiliary variables to share with its neighbors and estimate the aggregate function, so that the important information such as cost functions, constraints, and decisions are privatized. Based on fuzzy optimization and nonsmooth analysis, the asymptotic convergence of the algorithm to generalized Nash equilibrium is rigorously proved, and the convergence is not affected by the initial strategy profile of the players. Moreover, two application instances are used to demonstrate the theoretical results.