Cristiani, Emiliano, Piccoli, Benedetto, Tosin, Andrea
This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns...
Entropy type conditions for Riemann solvers at nodes (2009)
Garavello, Mauro, Piccoli, Benedetto
This paper deals with conservation laws on networks, represented by graphs. Entropy-type conditions are considered to determine dynamics at nodes. Since entropy dispersion is a local concept, we...
Effects of anisotropic interactions on the structure of animal groups (2009)
Cristiani, Emiliano, Frasca, Paolo, Piccoli, Benedetto
This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each...
Detection of Gaussian signals via hexagonal sensor networks (2009)
Frasca, Paolo, Mason, Paolo, Piccoli, Benedetto
This paper considers a special case of the problem of identifying a static scalar signal, depending on the location, using a planar network of sensors in a distributed fashion. Motivated by the...
Time Optimal Swing-Up of the Planar Pendulum (2008)
Mireille E. Broucke, Paolo Mason, Benedetto Piccoli
This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.
Pedestrian flows in bounded domains with obstacles (2008)
Piccoli, Benedetto, Tosin, Andrea
In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time...
Time-evolving measures and macroscopic modeling of pedestrian flow (2008)
Piccoli, Benedetto, Tosin, Andrea
This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic...
Improving efficiency of finite plans by optimal choice (2008)
Antonio Bicchi, Alessia Marigo, Benedetto Piccoli
of input sets
Discrete and Hybrid Nonholonomy ⋆ (2008)
Antonio Bicchi, Alessia Marigo, Benedetto Piccoli
Abstract. In this paper we consider the generalization of the classical notion of nonholonomy of smooth constraints in analytical mechanics, to a substantially wider set of systems, allowing for...
Fast algorithms for the approximation of a fluid-dynamic (2008)
Gabriella Bretti, Roberto Natalini, Benedetto Piccoli
model on networks
Extremal synthesis and Morse property for minimum time (2007)
Piccoli, Benedetto, Boscain, Ugo
Academic year 1999/2000
Time optimal swing-up of the planar pendulum (2006)
Broucke, Mireille E., Mason, Paolo, Piccoli, Benedetto
This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.
Source-Destination Flow on a Road Network (2005)
Garavello, Mauro, Piccoli, Benedetto
We construct a model of traffic flow with sources and destinations on a roads network. The model is based on a conservation law for the density of traffic and on semilinear equations for traffic-type...
Traffic flow on a road network (2002)
Coclite, Giuseppe Maria, Piccoli, Benedetto, Garavello, Mauro
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network...
Hybrid necessary principle (2002)
Garavello, Mauro, Piccoli, Benedetto
Proceedings of IFAC Conference on Analysis and Design of Hybrid Systems, Saint Malo, France
Well-posedness of the Cauchy problem for n x n systems of conservation laws (2000)
Bressan, Alberto, Crasta, Graziano, Piccoli, Benedetto
Chapter 1 and 2
On the reachability of quantized control systems (2000)
Bicchi, Antonio, Marigo, Alessia, Piccoli, Benedetto
In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable...
Regular Synthesis and Sufficiency Conditions for Optimality (2000)
Piccoli, Benedetto, Sussmann, Hector J.
We propose a definition of "regular synthesis" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of "regular presynthesis."...
Reachability Analysis for a Class of Quantized Control Systems (2000)
Marigo, Alessia, Piccoli, Benedetto, Bicchi, Antonio
We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or...
Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws (1999)
Amadori, Debora, Baiti, Paolo, LeFloch, Philippe G., Piccoli, Benedetto
The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a...
Infinite time regular synthesis (1998)
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There...
Regular Synthesis and Sufficiency Conditions for Optimality (1998)
Benedetto Piccoli, Héctor J. Sussmann
We propose a definition of "regular synthesis," more general than those suggested by other authors such as Boltyanskii and Brunovsk'y, and an even more general notion of "regular...
Regular Synthesis and Sufficiency Conditions for Optimality (1998)
Benedetto Piccoli, Hector J. Sussmann
We propose a definition of "regular synthesis," more general than those suggested by other authors such as Boltyanskii and Brunovsk'y, and an even more general notion of "regular...
Well-posedness of the Cauchy problem for n × n Systems of Conservation Laws (1997)
Alberto Bressan, Graziano Crasta, Benedetto Piccoli
. This paper is concerned with the initial value problem for a strictly hyperbolic n \Theta n system of conservation laws in one space dimension: u t + \Theta F (u) x = 0; u(0; x) = ¯ u(x): () Each...
Some control problems for the pendulum (1995)
The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the...
A generic classification of time-optimal planar stabilizing feedbacks (1995)
Bressan, Alberto, Piccoli, Benedetto
Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence...
Time-Optimal Control Problem for the Swing and the Ski (1994)
This paper is concerned with a class of time-optimal control problems for the swing and the ski. We first consider the motion of a man standing on a swing. For simplicity, we neglect friction and air...
A Baire Category Approach to the Bang-Bang Property (1992)
Bressan, Alberto, Piccoli, Benedetto
Aim of this paper is to develop a new technique, based on the Baire category theorem, in order to establish the closure of reachable sets and the existence of optimal trajectories for control...
Stabilità strutturale per un problema di tempo minimo (1991)
Il seguente lavoro studia la stabilità strutturale e la classificazione nell'ambito del problema di stabilizzazione in tempo minimo per sistemi di controllo sul piano.