Related papers: A Mean Field Games approach for multi-lane traffic…
Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…
Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…
We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…
In this paper we consider the application of Stackelberg game theory to model discretionary lane-changing in lightly congested highway setting. The fundamental intent of this model, which is parameterized to capture driver disposition…
We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the…
Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work…
We propose a hybrid decision-making framework for safe and efficient autonomous driving of selfish vehicles on highways. Specifically, we model the dynamics of each vehicle as a Mixed-Logical-Dynamical system and propose simple driving…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…
We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a…
Motivated by the need to develop simulation tools for verification and validation of autonomous driving systems operating in traffic consisting of both autonomous and human-driven vehicles, we propose a framework for modeling vehicle…
This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the…
Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…
This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our…
The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…
Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the…
We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We…