CDC 2018 Workshop: Traffic Flow Control via PDE Techniques
(https://cdc2018.ieeecss.org/workshops.php)
Date, Time, and Location: Sunday, December 16, 2018, 8:30 am -- 5:15 pm, Room: Splash 10, Fontainebleau Hotel, Miami Beach, FL, USA.
Program
Registration
Organizers
Nikolaos Bekiaris-Liberis, Technical University of Crete.
Maria Laura Delle Monache, Inria.
Delphine Bresch-Pietri, MINES ParisTech.
Rafael Vazquez, University of Seville.
Objectives
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 traffic – Miroslav 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 flow – Christophe 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 limits – Iasson 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 vehicles – Benedetto 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
vehicles – Paola 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 vehicles
– Gabor 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 control – Christian 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.