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Nonlinear hyperbolic partial differential equations govern continuum traffic flow models. Higher-order traffic flow models consisting of continuum equations and velocity dynamics were introduced to address the limitations of the Lighthill,…

Analysis of PDEs · Mathematics 2024-07-10 Nandan Maiti , Bhargava Rama Chilukuri

Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability…

Systems and Control · Electrical Eng. & Systems 2022-03-24 Tongjia Zheng , Qing Han , Hai Lin

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two…

Statistical Mechanics · Physics 2009-10-31 Vladislav Popkov , Ingo Peschel

We consider a discrete-time dynamical system in a car-following context. The system was recently introduced to parsimoniously model human driving behavior based on utility maximization. The parameters of the model were calibrated using…

Systems and Control · Electrical Eng. & Systems 2025-09-16 Suzhou Huang , Jian Hu

Human drivers may behave in an imprecise/unstable manner, leading to traffic oscillations which are harmful to traffic throughput. Recent field experiments have shown that the control of a single autonomous vehicle (AV) can increase traffic…

Systems and Control · Electrical Eng. & Systems 2019-12-04 Ronan L. Keane , H. Oliver Gao

Traffic congestion in dense urban centers presents an economical and environmental burden. In recent years, the availability of vehicle-to-anything communication allows for the transmission of detailed vehicle states to the infrastructure…

We propose a new model for multi-lane traffic with moving bottlenecks, e.g., autonomous vehicles (AV). It consists of a system of balance laws for traffic in each lane, coupled in the source terms for lane changing, and fully coupled to…

Analysis of PDEs · Mathematics 2024-04-29 Paola Goatin , Benedetto Piccoli

We address the traffic light control problem for a single intersection by viewing it as a stochastic hybrid system and developing a Stochastic Flow Model (SFM) for it. We adopt a quasi-dynamic control policy based on partial state…

Systems and Control · Computer Science 2013-08-06 Yanfeng Geng , Christos G. Cassandras

We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…

Popular Physics · Physics 2007-05-23 Dirk Helbing , Stefan Lämmer , Jean-Patrick Lebacque

We consider the problem of output feedback regulationfor a linear first-order hyperbolic system with collocatedinput and output in presence of a general class of disturbancesand noise. The proposed control law is designed through…

Analysis of PDEs · Mathematics 2017-10-20 Pierre-Olivier Lamare , Jean Auriol , Florent Di Meglio , Ulf Jakob F. Aarsnes

In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density…

Analysis of PDEs · Mathematics 2012-08-08 Florent Berthelin , Damien Broizat

Transitions between two lanes often have a significant impact on various forms of road traffic. To address this problem, we have developed a two-lane asymmetric simple exclusion process model and two hypothetical traffic control strategies,…

Physics and Society · Physics 2022-12-14 Yuming Dong , Xiaolu Jia , Daichi Yanagisawa , Akihito Nagahama , Katsuhiro Nishinari

A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a…

Optimization and Control · Mathematics 2020-05-01 Martin A Sehr , Robert R Bitmead

Traffic Signal Control (TSC) aims to reduce the average travel time of vehicles in a road network, which in turn enhances fuel utilization efficiency, air quality, and road safety, benefiting society as a whole. Due to the complexity of…

Computer Vision and Pattern Recognition · Computer Science 2023-06-14 Junfan Lin , Yuying Zhu , Lingbo Liu , Yang Liu , Guanbin Li , Liang Lin

As a strategy to reduce travel delay and enhance energy efficiency, platooning of connected and autonomous vehicles (CAVs) at non-signalized intersections has become increasingly popular in academia. However, few studies have attempted to…

Machine Learning · Computer Science 2022-06-28 Duowei Li , Jianping Wu , Feng Zhu , Tianyi Chen , Yiik Diew Wong

We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…

Analysis of PDEs · Mathematics 2016-12-13 Agus Hasan

Reinforcement learning (RL) holds significant promise for adaptive traffic signal control. While existing RL-based methods demonstrate effectiveness in reducing vehicular congestion, their predominant focus on vehicle-centric optimization…

Machine Learning · Computer Science 2025-07-24 Bibek Poudel , Xuan Wang , Weizi Li , Lei Zhu , Kevin Heaslip

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…

Statistical Mechanics · Physics 2009-11-07 Dirk Helbing , Davide Batic , Martin Schoenhof , Martin Treiber

We consider $\hinf$-optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal…

Optimization and Control · Mathematics 2026-04-07 Sachin Shivakumar , Amritam Das , Matthew Peet
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