Papers by Benedetto Piccoli
Axioms, Feb 7, 2021
Bookmarks Related papers MentionsView impact
Control Problems for Conservation Laws with Traffic Applications
Conservation and/or balance laws on networks in the recent years have been the subject of intense... more Conservation and/or balance laws on networks in the recent years have been the subject of intense study, since a wide range of different applications in real life can be covered by such a research.
Bookmarks Related papers MentionsView impact
Control Problems for Conservation Laws with Traffic Applications
A vehicle with different (eventually controlled) dynamics from general traffic along a street may... more A vehicle with different (eventually controlled) dynamics from general traffic along a street may reduce the road capacity, thus generating a moving bottleneck, and can be used to act on the traffic flow. The interaction between the controlled vehicle and the surrounding traffic, and the consequent flow reduction at the bottleneck position, can be described either by a conservation law with space dependent flux function [200], or by a strongly coupled PDE-ODE system proposed in [112, 208].
Bookmarks Related papers MentionsView impact
Axioms, 2021
This paper uses empirical traffic data collected from three locations in Europe and the US to rev... more This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models and could significantly impact travel time estimation on highways.
Bookmarks Related papers MentionsView impact
Journal of Differential Equations, 2020
Bookmarks Related papers MentionsView impact
Communications in Mathematical Sciences, 2018
Bookmarks Related papers MentionsView impact
Transportmetrica B: Transport Dynamics, 2015
Bookmarks Related papers MentionsView impact
Mathematical Models and Methods in Applied Sciences, 2017
We consider nonlinear transport equations with non-local velocity describing the time-evolution o... more We consider nonlinear transport equations with non-local velocity describing the time-evolution of a measure. Such equations often appear when considering the mean-field limit of finite-dimensional systems modeling collective dynamics. We address the problem of controlling these equations by means of a time-varying bounded control action localized on a time-varying control subset of small Lebesgue measure. We first define dissipativity for nonlinear transport equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, assuming that the uncontrolled system is dissipative, we provide an explicit construction of a control law steering the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function. In this sense the construction can be seen as an infinite-dimensional analogue of the well-known Jurdjevic–Quinn procedure. Moreover, the control l...
Bookmarks Related papers MentionsView impact
Transportation Research Part B: Methodological, 2016
Bookmarks Related papers MentionsView impact
Automatica, 2017
Bookmarks Related papers MentionsView impact
Active Particles, Volume 1, 2017
Bookmarks Related papers MentionsView impact
Procedia - Social and Behavioral Sciences, 2012
Bookmarks Related papers MentionsView impact
Mathematical Control & Related Fields, 2013
Bookmarks Related papers MentionsView impact
Mathematical Models and Methods in Applied Sciences, 2015
Starting with the seminal papers of Reynolds (1987), Vicsek et al. (1995), Cucker–Smale (2007), t... more Starting with the seminal papers of Reynolds (1987), Vicsek et al. (1995), Cucker–Smale (2007), there has been a lot of recent works on models of self-alignment and consensus dynamics. Self-organization has so far been the main driving concept of this research direction. However, the evidence that in practice self-organization does not necessarily occur (for instance, the achievement of unanimous consensus in government decisions) leads to the natural question of whether it is possible to externally influence the dynamics in order to promote the formation of certain desired patterns. Once this fundamental question is posed, one is also faced with the issue of defining the best way of obtaining the result, seeking for the most "economical" way to achieve a certain outcome. Our paper precisely addressed the issue of finding the sparsest control strategy in order to lead us optimally towards a given outcome, in this case the achievement of a state where the group will be able...
Bookmarks Related papers MentionsView impact
Networks & Heterogeneous Media, 2006
Bookmarks Related papers MentionsView impact
EMS Surveys in Mathematical Sciences, 2014
Bookmarks Related papers MentionsView impact
Contemporary Mathematics, 1999
Bookmarks Related papers MentionsView impact
SIAM Journal on Scientific Computing, 2011
Bookmarks Related papers MentionsView impact
SIAM Journal on Applied Mathematics, 2011
Bookmarks Related papers MentionsView impact
SIAM Journal on Applied Dynamical Systems, 2008
Bookmarks Related papers MentionsView impact
Uploads
Papers by Benedetto Piccoli