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We derive new results regarding the controllability and the reachability of multitime controlled linear PDE systems of first order. These systems describe some important multitime evolution in engineering, economics and biology. Some of…

Optimization and Control · Mathematics 2012-01-04 Cristian Ghiu , Constantin Udriste

Technology of autonomous vehicles (AVs) is getting mature and many AVs will appear on the roads in the near future. AVs become connected with the support of various vehicular communication technologies and they possess high degree of…

Systems and Control · Computer Science 2016-10-06 Albert Y. S. Lam , Yiu-Wing Leung , Xiaowen Chu

We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic…

Analysis of PDEs · Mathematics 2021-02-18 Jan Haskovec , Lisa Maria Kreusser , Peter Markowich

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the…

Statistical Mechanics · Physics 2015-05-19 C. Appert-Rolland , H. J. Hilhorst , G. Schehr

In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…

Mathematical Physics · Physics 2020-08-19 Irene M. Gamba , Milana Pavić-Čolić

Vehicles in developing countries have widely varying dimensions and speeds, and drivers tend to not follow lane discipline. In this flow state called "mixed traffic", the interactions between drivers and the resulting maneuvers resemble…

Physics and Society · Physics 2018-08-01 Venkatesan Kanagaraj , Martin Treiber

The purpose of this review paper is to present some recent results on the modeling and control of large systems of agents. We focus on particular applications where the agents are capable of independent actions instead of simply reacting to…

Optimization and Control · Mathematics 2023-02-27 Benedetto Piccoli

The integration of Automated Vehicles (AVs) into traffic flow holds the potential to significantly improve traffic congestion by enabling AVs to function as actuators within the flow. This paper introduces an adaptive speed controller…

Systems and Control · Electrical Eng. & Systems 2024-08-20 Han Wang , Hossein Nick Zinat Matin , Maria Laura Delle Monache

Connected and automated vehicles (CAVs) provide the most intriguing opportunity to optimize energy consumption and travel time. Several approaches have been proposed in the literature that allow CAVs to coordinate in situations where there…

Optimization and Control · Mathematics 2021-06-11 A M Ishtiaque Mahbub , Andreas A. Malikopoulos , Liuhui Zhao

We extend the classical LWR traffic model allowing different maximal speeds to different vehicles. Then, we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macro- scopic model displaying 2 phases,…

Analysis of PDEs · Mathematics 2009-09-16 Rinaldo M. Colombo , Francesca Marcellini , Michel Rascle

The limiting case of the system of equations of two-dimensional gas dynamics in the presence of the Coriolis force, which can be obtained under the assumption of a small pressure, is considered. With this approach, the equation for the…

Analysis of PDEs · Mathematics 2019-09-19 Olga Rozanova , Olga Uspenskaya

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be…

In this article, we present a long-duration autonomy approach for the control of connected and automated vehicles (CAVs) operating in a transportation network. In particular, we focus on the performance of CAVs at traffic bottlenecks,…

Systems and Control · Electrical Eng. & Systems 2025-10-10 Logan E. Beaver

We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…

Probability · Mathematics 2019-12-13 Simone Göttlich , Stephan Knapp

A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…

Dynamical Systems · Mathematics 2016-08-12 Laura Hattam

Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…

Optimization and Control · Mathematics 2010-02-11 Nadir Farhi

We demonstrate that in Optimal Velocity Model (OVM) delay times of vehicles coming from the dynamical equation of motion of OVM almost explain the order of delay times observed in actual traffic flows without introducing explicit delay…

patt-sol · Physics 2008-02-03 Masako Bando , Katsuya Hasebe , Ken Nakanishi , Akihiro Nakayama

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends…

Analysis of PDEs · Mathematics 2024-05-06 Abraham Sylla

We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two…

Analysis of PDEs · Mathematics 2018-02-14 Edda Dal Santo , Massimiliano D. Rosini , Nikodem Dymski , Mohamed Benyahia

The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…

Physics and Society · Physics 2015-04-10 Tal Cohen , Rohan Abeyaratne