Related papers: Autonomous Vehicles Driving Traffic: The Cauchy Pr…
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…
When connected and autonomous vehicles (CAVs) are widely used in the future, we can foresee many essential applications, such as platoon formation and autonomous police patrolling, which need two CAVs, originally separated in a mixed…
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…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…
Autonomous driving has been the subject of increased interest in recent years both in industry and in academia. Serious efforts are being pursued to address legal, technical and logistical problems and make autonomous cars a viable option…
We consider an agro-ecologically motivated coupling between a prey-predator system and a vector-borne epidemic system. The coupled system contains one ODE, two reaction-diffusion PDEs and one reaction-diffusionadvection PDE; it has no…
In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) at different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its…
We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…
This work proposes a solution for the longitudinal and lateral control problem of urban autonomous vehicles using a gain scheduling LPV control approach. Using the kinematic and dynamic vehicle models, a linear parameter varying (LPV)…
Urbanization and technological advancements are reshaping urban mobility, presenting both challenges and opportunities. This paper investigates how Artificial Intelligence (AI)-driven technologies can impact traffic congestion dynamics and…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
Adaptive-Cruise Control (ACC) automatically accelerates or decelerates a vehicle to maintain a selected time gap, to reach a desired velocity, or to prevent a rear-end collision. To this end, the ACC sensors detect and track the vehicle…
This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs…
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state…
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…
Connected and automated vehicles (CAVs) rely on wireless communication to exchange state information for distributed control, making communication delays a critical factor that can affect vehicle motion and degrade control performance,…
Interactions between pedestrians, bikers, and human-driven vehicles have been a major concern in traffic safety over the years. The upcoming age of autonomous vehicles will further raise major problems on whether self-driving cars can…
The emergence of autonomous vehicles is expected to revolutionize road transportation in the near future. Although large-scale numerical simulations and small-scale experiments have shown promising results, a comprehensive theoretical…