Related papers: Approximate Dynamic Programming for a Mean-field G…
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…
The design of an automated vehicle controller can be generally formulated into an optimal control problem. This paper proposes a continuous-time finite-horizon approximate dynamicprogramming (ADP) method, which can synthesis off-line…
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…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
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…
We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…
We address a multi-class traffic model, for which we computationally assess the ability of mean-field games (MFGs) to yield approximate Nash equilibria for traffic flow games of intractable large finite-players. We introduce ad hoc…
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)…
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…
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…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…
In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…
Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of…
It is well known that stop-and-go waves can be generated spontaneously in traffic even without bottlenecks. Can such undesirable traffic patterns, induced by intrinsic human driving behaviors, be tamed effectively and inexpensively? Taking…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
We use a very simple description of human driving behavior to simulate traffic. The regime of maximum vehicle flow in a closed system shows near-critical behavior, and as a result a sharp decrease of the predictability of travel time. Since…
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…
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…