arXiv subjects

Benedetto Piccoli

Publications and source records attributed to Benedetto Piccoli.

At least 19 recordsLinked to original sources

arXiv2026

Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow

This work provides a traffic flow interpretation of the model recently introduced in \cite{ABS2025}. We adapt the conservation law with discontinuous gradient-dependent flux to a macroscopic traffic setting, assuming concave flux functions $f(u)$ and $g(u)$ defined on the density domain $[0,u_{\max}]$. To prevent violations of the maximal density constraint, we introduce modified Riemann Solvers tailored to this setting and generalize the existence theory for weak solutions developed in \cite{ABS2025}. Finally, we construct Riemann Solvers for a broader two-phase model incorporating a free-flow regime, in which $f(u)=g(u)$ on a subset of $[0,u_{\max}]$, and establish existence of weak solutions in this more general framework.

math.AP↗

arXiv2026

Emission reduction potential of freeway stop-and-go wave smoothing

The real-world potential of stop-and-go wave smoothing at scale remains largely unquantified. Smoothing freeway waves requires opening a gap large enough for them to dissipate, but that gap is often impractically large. We propose a counterfactual wave-smoothing benchmark that reconstructs a smooth, feasible trajectory from each empirical trajectory by solving a quadratic program with fixed boundary conditions and a maximum-gap constraint, and we use the MOVES model to estimate the resulting emission reduction potential. Applying the framework to nine weeks of weekday peak-period data from the I-24 MOTION testbed, which exhibits rich day-to-day variation in wave dynamics, we find meaningful potential for passenger cars under a 0.1-mile maximum-gap constraint: average CO2 reductions of 9.80% to 14.08% across lanes, with 12.94% to 25.70% in CO, 24.29% to 29.76% in HC, and 29.40% to 36.03% in NOx. Trucks emerge as particularly attractive targets, showing roughly twice the reduction potential of passenger cars.

eess.SY↗

arXiv2026

Properties of Measure Controls and Their Trajectories

This paper deals with the concepts of measure controls and of measure vector fields, within the mathematical framework of measure differential equations (MDEs), recently proposed in~\cite{piccoli_measure_2019}. Measure controls can be seen as a generalization of relaxed control. Moreover, they are particularly suitable for studying dynamics with uncertainty. The main results of this paper include establishing the existence and well-posedness of control systems with measure controls and proving the equivalence between measure controls and measure vector fields. The stability and closure properties of the trajectory set are also studied.

math.OC↗

arXiv2026

Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs

We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative structure of the scheme. The model can be trained both in a supervised setting with efficiently generated synthetic data or in an unsupervised manner, leveraging the weak formulation of the partial differential equation. We provide theoretical results that our model can perform arbitrarily well, and provide associated upper bounds on neural network size. Extensive experiments demonstrate that our method often outperforms efficient schemes such as Godunov's scheme, WENO, and Discontinuous Galerkin for comparable computational budgets. Finally, we demonstrate the effectiveness of our method on a traffic prediction task, leveraging field experimental highway data from the Berkeley DeepDrive drone dataset.

math.NA↗

arXiv2025

Hybrid multi-population traffic flow model: Optimal control for a mean-field limit

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) and autonomous vehicles, the latter characterized by controlled acceleration. Compared to single-population models, multi-population modeling poses greater challenges, primarily due to the increased number of parameters required to describe lane-changing behavior and the added complexity in passing to the mean-field limit. We model multi-lane traffic as a hybrid dynamical system, combining continuous dynamics within each lane and discrete events corresponding to lane-changing maneuvers. We then formulate and analyze the optimal control problem associated with such hybrid systems from both microscopic and mesoscopic perspectives. Using techniques from $Γ$-convergence, we prove the existence of solutions to the optimal control problem in the mean-field limit of a finite-dimensional hybrid system. Finally, we present numerical simulations illustrating the impact of trucks on overall traffic efficiency.

math.OC↗

arXiv2025

Scalable analysis of stop-and-go waves: Representation, measurements and insights

Analyzing stop-and-go waves at the scale of miles and hours of data is an emerging challenge in traffic research. The past 5 years have seen an explosion in the availability of large-scale traffic data containing traffic waves and complex congestion patterns, making existing approaches unsuitable for repeatable and scalable analysis of traffic waves in these data. This paper makes a first step towards addressing this challenge by introducing an automatic and scalable stop-and-go wave identification method capable of capturing wave generation, propagation, dissipation, as well as bifurcation and merging, which have previously been observed only very rarely. Using a concise and simple critical-speed based definition of a stop-and-go wave, the proposed method identifies all wave boundaries that encompass spatio-temporal points where vehicle speed is below a chosen critical speed. The method is built upon a graph representation of the spatio-temporal points associated with stop-and-go waves, specifically wave front (start) points and wave tail (end) points, and approaches the solution as a graph component identification problem. It enables the measurement of wave properties at scale. The method is implemented in Python and demonstrated on a large-scale dataset, I-24 MOTION INCEPTION. Our results show insights on the complexity of traffic waves. Traffic waves can bifurcate and merge at a scale that has never been observed or described before. The clustering analysis of all the identified wave components reveals the different topological structures of traffic waves. We explored that the wave merge or bifurcation points can be explained by spatial features. The gallery of all the identified wave topologies is demonstrated at https://trafficwaves.github.io/.

physics.soc-ph↗

arXiv2025

Stop-and-go wave super-resolution reconstruction via iterative refinement

Stop-and-go waves are a fundamental phenomenon in freeway traffic flow, contributing to inefficiencies, crashes, and emissions. Recent advancements in high-fidelity sensor technologies have improved the ability to capture detailed traffic dynamics, yet such systems remain scarce and costly. In contrast, conventional traffic sensors are widely deployed but suffer from relatively coarse-grain data resolution, potentially impeding accurate analysis of stop-and-go waves. This article explores whether generative AI models can enhance the resolution of conventional traffic sensor to approximate the quality of high-fidelity observations. We present a novel approach using a conditional diffusion denoising model, designed to reconstruct fine-grained traffic speed field from radar-based conventional sensors via iterative refinement. We introduce a new dataset, I24-WaveX, comprising 132 hours of data from both low and high-fidelity sensor systems, totaling over 2 million vehicle miles traveled. Our approach leverages this dataset to formulate the traffic measurement enhancement problem as a spatio-temporal super-resolution task. We demonstrate that our model can effectively reproduce the patterns of stop-and-go waves, achieving high accuracy in capturing these critical traffic dynamics. Our results show promising advancements in traffic data enhancement, offering a cost-effective way to leverage existing low spatio-temporal resolution sensor networks for improved traffic analysis and management. We also open-sourced our trained model and code to facilitate further research and applications.

eess.SY↗

arXiv2025

Car-Following Models: A Multidisciplinary Review

Car-following (CF) algorithms are crucial components of traffic simulations and have been integrated into many production vehicles equipped with Advanced Driving Assistance Systems (ADAS). Insights from the model of car-following behavior help us understand the causes of various macro phenomena that arise from interactions between pairs of vehicles. Car-following models encompass multiple disciplines, including traffic engineering, physics, dynamic system control, cognitive science, machine learning, and reinforcement learning. This paper presents an extensive survey that highlights the differences, complementarities, and overlaps among microscopic traffic flow and control models based on their underlying principles and design logic. It reviews representative algorithms, ranging from theory-based kinematic models, Psycho-Physical Models, and Adaptive cruise control models to data-driven algorithms like Reinforcement Learning (RL) and Imitation Learning (IL). The manuscript discusses the strengths and limitations of these models and explores their applications in different contexts. This review synthesizes existing researches across different domains to fill knowledge gaps and offer guidance for future research by identifying the latest trends in car following models and their applications.

eess.SY↗

arXiv2024

Adapting Priority Riemann Solver for GSOM on road networks

In this paper, we present an extension of the Generic Second Order Models (GSOM) for traffic flow on road networks. We define a Riemann solver at the junction based on a priority rule and provide an iterative algorithm to construct solutions at junctions with n incoming and m outgoing roads. The logic underlying our solver is as follows: the flow is maximized while respecting the priority rule, which can be adjusted if the supply of an outgoing road exceeds the demand of a higher-priority incoming road. Approximate solutions for Cauchy problems are constructed using wave-front tracking. We establish bounds on the total variation of waves interacting with the junction and present explicit calculations for junctions with two incoming and two outgoing roads. A key novelty of this work is the detailed analysis of returning waves - waves generated at the junction that return to the junction after interacting along the roads - which, in contrast to first-order models such as LWR, can increase flux variation.

math.AP↗

arXiv2024

Reinforcement Learning Based Oscillation Dampening: Scaling up Single-Agent RL algorithms to a 100 AV highway field operational test

In this article, we explore the technical details of the reinforcement learning (RL) algorithms that were deployed in the largest field test of automated vehicles designed to smooth traffic flow in history as of 2023, uncovering the challenges and breakthroughs that come with developing RL controllers for automated vehicles. We delve into the fundamental concepts behind RL algorithms and their application in the context of self-driving cars, discussing the developmental process from simulation to deployment in detail, from designing simulators to reward function shaping. We present the results in both simulation and deployment, discussing the flow-smoothing benefits of the RL controller. From understanding the basics of Markov decision processes to exploring advanced techniques such as deep RL, our article offers a comprehensive overview and deep dive of the theoretical foundations and practical implementations driving this rapidly evolving field. We also showcase real-world case studies and alternative research projects that highlight the impact of RL controllers in revolutionizing autonomous driving. From tackling complex urban environments to dealing with unpredictable traffic scenarios, these intelligent controllers are pushing the boundaries of what automated vehicles can achieve. Furthermore, we examine the safety considerations and hardware-focused technical details surrounding deployment of RL controllers into automated vehicles. As these algorithms learn and evolve through interactions with the environment, ensuring their behavior aligns with safety standards becomes crucial. We explore the methodologies and frameworks being developed to address these challenges, emphasizing the importance of building reliable control systems for automated vehicles.

eess.SY↗

arXiv2024

A multi-scale multi-lane model for traffic regulation via autonomous vehicles

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 ODEs for the AVs' trajectories.More precisely, each AV solves a controlled equation depending on the traffic density, while the PDE on the corresponding lane has a flux constraint at the AV's location. We prove existence of entropy weak solutions, and we characterize the limiting behavior for the source term converging to zero (without AVs), corresponding to a scalar conservation law for the total density.The convergence in the presence of AVs is more delicate and we show that the limit does not satisfy an entropic equation for the total density as in the original coupled ODE-PDE model. Finally, we illustrate our results via numerical simulations.

math.AP↗

arXiv2024

Designing, simulating, and performing the 100-AV field test for the CIRCLES consortium: Methodology and Implementation of the Largest mobile traffic control experiment to date

Previous controlled experiments on single-lane ring roads have shown that a single partially autonomous vehicle (AV) can effectively mitigate traffic waves. This naturally prompts the question of how these findings can be generalized to field operational, high-density traffic conditions. To address this question, the Congestion Impacts Reduction via CAV-in-the-loop Lagrangian Energy Smoothing (CIRCLES) Consortium conducted MegaVanderTest (MVT), a live traffic control experiment involving 100 vehicles near Nashville, TN, USA. This article is a tutorial for developing analytical and simulation-based tools essential for designing and executing a live traffic control experiment like the MVT. It presents an overview of the proposed roadmap and various procedures used in designing, monitoring, and conducting the MVT, which is the largest mobile traffic control experiment at the time. The design process is aimed at evaluating the impact of the CIRCLES AVs on surrounding traffic. The article discusses the agent-based traffic simulation framework created for this evaluation. A novel methodological framework is introduced to calibrate this microsimulation, aiming to accurately capture traffic dynamics and assess the impact of adding 100 vehicles to existing traffic. The calibration model's effectiveness is verified using data from a six-mile section of Nashville's I-24 highway. The results indicate that the proposed model establishes an effective feedback loop between the optimizer and the simulator, thereby calibrating flow and speed with different spatiotemporal characteristics to minimize the error between simulated and real-world data. Finally, We simulate AVs in multiple scenarios to assess their effect on traffic congestion. This evaluation validates the AV routes, thereby contributing to the execution of a safe and successful live traffic control experiment via AVs.

eess.SY↗

arXiv2024

Hierarchical Speed Planner for Automated Vehicles: A Framework for Lagrangian Variable Speed Limit in Mixed Autonomy Traffic

This paper introduces a novel control framework for Lagrangian variable speed limits in hybrid traffic flow environments utilizing automated vehicles (AVs). The framework was validated using a fleet of 100 connected automated vehicles as part of the largest coordinated open-road test designed to smooth traffic flow. The framework includes two main components: a high-level controller deployed on the server side, named Speed Planner, and low-level controllers called vehicle controllers deployed on the vehicle side. The Speed Planner designs and updates target speeds for the vehicle controllers based on real-time Traffic State Estimation (TSE) [1]. The Speed Planner comprises two modules: a TSE enhancement module and a target speed design module. The TSE enhancement module is designed to minimize the effects of inherent latency in the received traffic information and to improve the spatial and temporal resolution of the input traffic data. The target speed design module generates target speed profiles with the goal of improving traffic flow. The vehicle controllers are designed to track the target speed meanwhile responding to the surrounding situation. The numerical simulation indicates the performance of the proposed method: the bottleneck throughput has increased by 5.01%, and the speed standard deviation has been reduced by a significant 34.36%. We further showcase an operational study with a description of how the controller was implemented on a field-test with 100 AVs and its comprehensive effects on the traffic flow.

eess.SY↗

arXiv2024

Traffic Control via Connected and Automated Vehicles: An Open-Road Field Experiment with 100 CAVs

The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. These "phantom jams" or "stop-and-go waves,"are a significant source of wasted energy. Toward this goal, the CIRCLES project designed a control system referred to as the MegaController by the CIRCLES team, that could be deployed in real traffic. Our field experiment leveraged a heterogeneous fleet of 100 longitudinally-controlled vehicles as Lagrangian traffic actuators, each of which ran a controller with the architecture described in this paper. The MegaController is a hierarchical control architecture, which consists of two main layers. The upper layer is called Speed Planner, and is a centralized optimal control algorithm. It assigns speed targets to the vehicles, conveyed through the LTE cellular network. The lower layer is a control layer, running on each vehicle. It performs local actuation by overriding the stock adaptive cruise controller, using the stock on-board sensors. The Speed Planner ingests live data feeds provided by third parties, as well as data from our own control vehicles, and uses both to perform the speed assignment. The architecture of the speed planner allows for modular use of standard control techniques, such as optimal control, model predictive control, kernel methods and others, including Deep RL, model predictive control and explicit controllers. Depending on the vehicle architecture, all onboard sensing data can be accessed by the local controllers, or only some. Control inputs vary across different automakers, with inputs ranging from torque or acceleration requests for some cars, and electronic selection of ACC set points in others. The proposed architecture allows for the combination of all possible settings proposed above. Most configurations were tested throughout the ramp up to the MegaVandertest.

eess.SY↗

arXiv2023

Enabling Mixed Autonomy Traffic Control

We demonstrate a new capability of automated vehicles: mixed autonomy traffic control. With this new capability, automated vehicles can shape the traffic flows composed of other non-automated vehicles, which has the promise to improve safety, efficiency, and energy outcomes in transportation systems at a societal scale. Investigating mixed autonomy mobile traffic control must be done in situ given that the complex dynamics of other drivers and their response to a team of automated vehicles cannot be effectively modeled. This capability has been blocked because there is no existing scalable and affordable platform for experimental control. This paper introduces an extensible open-source hardware and software platform, enabling a team of 100 vehicles to execute several different vehicular control algorithms as a collaborative fleet, composed of three different makes and models, which drove 22752 miles in a combined 1022 hours, over 5 days in Nashville, TN in November 2022.

cs.RO↗

arXiv2023

Traffic smoothing using explicit local controllers

The dissipation of stop-and-go waves attracted recent attention as a traffic management problem, which can be efficiently addressed by automated driving. As part of the 100 automated vehicles experiment named MegaVanderTest, feedback controls were used to induce strong dissipation via velocity smoothing. More precisely, a single vehicle driving differently in one of the four lanes of I-24 in the Nashville area was able to regularize the velocity profile by reducing oscillations in time and velocity differences among vehicles. Quantitative measures of this effect were possible due to the innovative I-24 MOTION system capable of monitoring the traffic conditions for all vehicles on the roadway. This paper presents the control design, the technological aspects involved in its deployment, and, finally, the results achieved by the experiment.

eess.SY↗

arXiv2023

So you think you can track?

This work introduces a multi-camera tracking dataset consisting of 234 hours of video data recorded concurrently from 234 overlapping HD cameras covering a 4.2 mile stretch of 8-10 lane interstate highway near Nashville, TN. The video is recorded during a period of high traffic density with 500+ objects typically visible within the scene and typical object longevities of 3-15 minutes. GPS trajectories from 270 vehicle passes through the scene are manually corrected in the video data to provide a set of ground-truth trajectories for recall-oriented tracking metrics, and object detections are provided for each camera in the scene (159 million total before cross-camera fusion). Initial benchmarking of tracking-by-detection algorithms is performed against the GPS trajectories, and a best HOTA of only 9.5% is obtained (best recall 75.9% at IOU 0.1, 47.9 average IDs per ground truth object), indicating the benchmarked trackers do not perform sufficiently well at the long temporal and spatial durations required for traffic scene understanding.

cs.CV↗

arXiv2023

Control of multi-agent systems: results, open problems, and applications

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 external forces. In the literature, such agents were referred to as autonomous, intelligent, self-propelled, greedy, and others. The main applications we have in mind are social systems (as opinion dynamics), pedestrian movements (also called crowd dynamics), animal groups, and vehicular traffic. Also, the control problems posed by such systems are new and require innovative methods. We illustrate some ideas, developed recently, including the use of sparse controls, limiting the total variation of controls, and defining new control problems for measures. After reviewing various approaches, we discuss some future research directions of potential interest. The latter encompasses both new types of equations, as well as new types of limiting procedures to connect several scales at which a system can be represented. We conclude by illustrating a recent real-life experiment using autonomous vehicles on an open highway to smooth traffic waves. This opens the door to a new era of interventions to control in real-time multi-agent systems and to increase the societal impact of such interventions guided by control research.

math.OC↗