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Highway vehicular traffic is an inherently multi-agent problem. Traffic jamscan appear and disappear mysteriously. We develop a method for traffic flowcontrol that is applied at the vehicular level via mean-field games. We beginthis work with a microscopic model of vehicles subject to control input,disturbances, noise, and a speed limit. We formulate a discounted-costinfinite-horizon robust mean-field game on the vehicles, and obtain theassociated dynamic programming (DP) PDE system. We then perform approximatedynamic programming (ADP) using these equations to obtain a sub-optimal controlfor the traffic density adaptively. The sub-optimal controls are subject to anODE-PDE system. We show that the ADP ODE-PDE system has a unique weak solutionin a suitable Hilbert space using semigroup and successive approximationmethods. We additionally give a numerical simulation, and interpret theresults.

Approximate Dynamic Programming for a Mean-field Game of Traffic Flow: Existence and Uniqueness