Distributed Algorithm for Robust Wardrop Equilibrium in Uncertain Aggregative Congestion Games

2026-05-31

AI Summary

This work addresses aggregative congestion games with uncertain coupled constraints by proposing a fully distributed algorithm to compute the robust generalized Wardrop equilibrium. The original problem is first reformulated into a deterministic augmented form via robust optimization, and for the first time, a distributed solution is achieved by integrating projected primal-dual dynamics with dynamic tracking techniques. Theoretically, the paper rigorously establishes the equivalence between the robust Wardrop equilibrium and the robust generalized Nash equilibrium, and proves algorithmic convergence using singular perturbation theory and LaSalle’s invariance principle. The effectiveness of the proposed method is empirically validated in a plug-in electric vehicle charging control scenario.

Abstract

This paper considers a class of aggregative congestion games with uncertain coupling constraints, and devises a distributed algorithm to seek the robust generalized Wardrop equilibrium (RGWE) under worst-case uncertainty. Utilizing robust optimization theory, we reformulate the original aggregative congestion game with uncertainty into a tractable and deterministic augmented problem. Building upon this reformulation, we design a fully distributed algorithm to seek the RGWE by integrating a projected primal-dual scheme and a dynamic tracking technique. The convergence of the proposed algorithm is rigorously guaranteed via singular perturbation theory and LaSalle's invariance principle. Furthermore, we explicitly characterize the relationship between the obtained RGWE and the robust generalized Nash equilibrium, as the latter captures full strategic interactions. Finally, numerical simulations on the charging control of plug-in electric vehicles corroborate our theoretical findings.

Problem

• aggregative congestion games
• uncertain coupling constraints
• robust Wardrop equilibrium
• worst-case uncertainty

Innovation

• robust optimization
• distributed algorithm
• aggregative congestion games
• Wardrop equilibrium
• dynamic tracking