CDC 2018 Workshop: Traffic Flow Control via PDE Techniques (

Date, Time, and Location: Sunday, December 16, 2018, 8:30 am -- 5:15 pm, Room: Splash 10, Fontainebleau Hotel, Miami Beach, FL, USA.

Nikolaos Bekiaris-Liberis, Technical University of Crete.
Maria Laura Delle Monache, Inria.
Delphine Bresch-Pietri, MINES ParisTech.
Rafael Vazquez, University of Seville.


One of the main goals of the workshop is the exposition of the most up-to-date advances in the development of methodologies for (vehicular) traffic flow control and estimation as well as for traffic flow dynamics modeling for control and estimation, with particular emphasis on techniques that are based on a PDE description of the traffic flow dynamics. The workshop includes presentations that address both methodological and practical aspects of traffic flow control, utilizing techniques for control of distributed parameter systems. In particular, the presentations of the workshop are concerned with the exposition of techniques based on PDE boundary control via backstepping and Lyapunov-based methods, indomain feedback control design methodologies, methods for control of PDE-ODE interconnections, including MPC, delay-compensating designs, measure-theoretic approaches, advanced statistical methods, and of efficient numerical schemes.

Another goal of the workshop is to bridge the gap between theory and practice of PDE-based traffic flow control techniques. For this reason, the presentations, besides including novel control design tools, they address specific traffic control problems, such as, mitigation of disturbing traffic waves (e.g., “stop-and-go” waves), reduction of fuel consumption, traffic congestion mitigation and travel times minimization, and safety improvement.

In addition, it is one of the workshop’s goals to include both classical traffic flow control approaches as well as future traffic management techniques. In particular, the workshop is divided into two different sessions, one that considers classical traffic control implementation approaches, such as, for example, ramp metering and variable speed limits, and another one that is dealing with traffic control in the presence of connected and automated vehicles.

Expected outcomes

One of the main expected outcomes of the workshop is the audience to become acquainted with the state-of-the-art of PDE-based traffic flow control methodologies. In particular, it is expected that the attendees acquire new knowledge of both methodologies for control and estimation of distributed parameter systems as well as for traffic flow control. After the end of the workshop, the audience will be aware of the challenges and open problems of PDE-based traffic flow control both from the methodological and practical viewpoints.

It is expected that the workshop is intriguing and highly motivating for researchers working on the theory of control of PDEs, for control practitioners who wish to expand their control design toolbox, and graduate students who are looking for new problems in a mathematically challenging and practically ubiquitous systems and control field. This is attributed to the fact that the workshop’s presentations cover all of the four different viewpoints of PDE-based traffic flow control, i.e., the “control theorist”, the “mathematician”, “the physicist”, and the “civil engineer” viewpoints. Moreover, it should be also mentioned that the worksop is well-balanced between theory and practice of PDE-based traffic flow control.

In addition, via the interaction between the workshop’s attendees and, particularly, between the speakers and the attendees, the workshop would be useful in establishing new connections among the participants, thus paving the way for new collaborations, which may be an important intermediate step toward the further advancement of the field.

Target audience, prerequisites, and attendance

The goal of the workshop is to attract both researchers interested in control of distributed parameter systems as well as researchers interested in control of traffic systems. Thus, the target audience consists of researchers from academia (at various seniority levels from graduate students to full professors) as well as control practitioners from industry, including, control theorists, mathematicians, and engineers.

There are no particular prerequisites for attendees and the workshop is self-contained, but some basic knowledge of linear/nonlinear systems and control theory would be useful.

The workshop incorporates presentations from a diverse group of researchers, with respect to their approaches & expertise, background & training, geographical location, and gender.

Titles and abstracts of the presentations

Calming “stop-and-go” in congested trafficMiroslav Krstic, University of California, San Diego, USA

“Stop-and-go” oscillations in congested traffic frustrate human drivers and may be aggravated with the presence of autonomous vehicles, unless their control algorithms are designed to promote “damping” rather than merely “safety” and caution. State-of-the-art traffic models are coupled nonlinear hyperbolic PDEs for density and velocity, like for gases, but also include elements of human behavior (“forward-oriented” attention, collision avoidance, etc.). Actuation by ramp metering (the durations of red and green lights) propagates, through human action, upstream, i.e., against the direction of the cars motion. I will show how PDE backstepping controllers stabilize stop-and-go, at large distances from the ramp, even in the absence of distributed measurements of vehicle speed and density, and when driver reaction times are unknown.

Recent advances on Lyapunov based control for traffic flowChristophe Prieur, CNRS, Gipsa-lab, France

In this presentation, I will review some recent results on the boundary control of traffic flow when using hyperbolic systems. Different kinds of stability will be considered such as asymptotic stability, stochastic stability and exponential stability with positive solutions. Lyapunov function techniques will be shown to be a common approach to solve the design problem of proportional (or integral-proportional) boundary controllers. Some numerical simulations will illustrate the results when modeling freeway traffic, in particular by integrating the on-ramp metering with the speed limit control. Joint work with Liguo Zhang.

Feedback control of scalar conservation laws with application to density control in freeways by means of variable speed limitsIasson Karafyllis, National Technical University of Athens, Greece

The talk provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are studied: the problem with free speed limits at the inlet and the problem with no speed limits at the inlet. Explicit formulas are provided for respective feedback laws that guarantee stabilization of the desired equilibrium profile. For the first problem, global asymptotic stabilization is achieved; while for the second problem, regional exponential stabilization is achieved. Moreover, the solutions for the corresponding closed-loop systems are guaranteed to be classical solutions, i.e., there are no shocks. The obtained results are illustrated by means of a numerical example. Joint work with Markos Papageorgiou.

Lagrangian controls for traffic flow with autonomous and connected vehiclesBenedetto Piccoli, Rutgers University, USA

CAVs (Connected and autonomous vehicles) introduce new control possibilities for traffic flow. Recently, a NSFfunded group showed how simple control algorithms can help dissipating traffic waves, which in turn are responsible for increased fuel consumption and braking events. We will revise the experiment results and illustrate the control problems relate to the study. In particular, we will discuss mixed ODE-PDE problems for CAVs immersed in bulk traffic and recent measure-theoretic approach to the problem via mean-field limits.

Macroscopic modeling of traffic control by autonomous vehiclesPaola Goatin, INRIA Sophia Antipolis, France

We present a coupled PDE-ODE model describing the interaction of a controlled vehicle with the surrounding traffic. The traffic flow is described by the classical LWR macroscopic model, while the velocity of the controlled vehicle, which acts as a control, adapts to the downstream traffic conditions. At the same time, the presence of the vehicle induces a moving bottleneck, hindering traffic flow. We prove existence of solutions via a wave-front tracking algorithm. We then apply a MPC (Model Predictive Control) algorithm to optimize the traffic flow in terms of fuel consumption minimization, showing that this also reduces the Average Travel Time and the queue length upstream a fixed bottleneck.

Mitigating traffic waves with connected automated vehiclesGabor Orosz, University of Michigan, Ann Arbor, USA

In this talk we discuss our recent results about utilizing wireless V2X information from within and beyond the line of sight in order to control the motion of connected automated vehicles in traffic. In particular we describe the a general framework called connected cruise control (CCC) which allows connected automated vehicles to integrate well in human-dominated traffic. We show that connected automated vehicles with appropriately designed CCC algorithms can mitigate traffic waves traveling along chains of humandriven vehicles, and thus, improve the safety and energy efficiency of themselves as well as the neighboring humandriven vehicles. That is, connected automated vehicles can improve human-dominated traffic flow while being integral part of the flow.

A fast semi-analytic algorithm for computing solutions associated with multiple fixed or mobile capacity restrictions: applications to bus holding controlChristian Claudel, University of Texas at Austin, USA

Moving and fixed bottlenecks are moving or fixed capacity restrictions that affect the propagation of traffic flow. They are a very important modeling approach to describe the effects of slow vehicles and traffic signals in transportation networks. However, the computation of solutions associated with the presence of fixed and moving bottlenecks is complex, since they both influence and are influenced by traffic. In this study, we propose a fast numerical scheme that can efficiently compute the solutions to an arbitrary number of fixed and moving bottlenecks, for a stretch of road modeled by the Lighthill-Whitham-Richards (LWR) model with triangular fundamental diagram. The numerical scheme is based on a semi-analytic Lax-Hopf formula that requires a very low number of operations compared with existing schemes. We illustrate the performance of this scheme on a realistic bus control problem in which the time headway of the buses is controlled to minimize delays for passengers and traffic disruptions.

Can big data help traffic flow control? – Maria Laura Delle Monache, INRIA Grenoble-Rhone Alpes, France

We propose novel methodologies to analyze traffic data from fixed sensors. The main aim is to understand traffic characteristics by looking at the fundamental diagram. The main novelties of our approach consist in the use advanced statistical methods to analyze traffic data. In particular, we analyze data from multiple location in United States and Europe to show different traffic regimes and how they are related even from different geographical location. Moreover, we analyze specific accidents data and study their impact on regular traffic conditions. We will propose strategies to mitigate traffic conditions in these situations by adopting adhoc control strategies.

Traffic flow control via PDEs: Delay-compensating and coordinated designs – Nikolaos Bekiaris-Liberis, Technical University of Crete, Greece

Input delays are ubiquitous in vehicular traffic systems. On a macroscopic level, delays may be caused by long distances between actuated on-ramps and bottleneck areas, whereas on a microscopic level, delays may be due to actuators or sensors. If the delay effect is not taken into account, it may, in the former case, lead to congestion, whereas in the latter, it may jeopardize string (or even individual vehicle) stability, resulting in both cases to increased travel times and fuel consumption. I will present predictor-feedback designs for delay compensation in both cases–in the former, via introduction of a predictor-feedback ramp metering strategy for quasilinear transport PDE-ODE interconnections and, in the latter, by showing that predictor-based ACC laws may also guarantee string stability. I will further present fault-tolerant feedback control designs for ramp metering or variable speed limits, via introduction of “bilateral” boundary control laws for viscous Hamilton-Jacobi PDEs, which interlace PDE feedback linearization with PDE backstepping.