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This paper establishes the continuity of the path delay operators for dynamic network loading (DNL) problems based on the Lighthill–Whitham–Richards model, which explicitly capture vehicle spillback. The DNL describes and predicts the... more
This paper establishes the continuity of the path delay operators for dynamic network loading (DNL) problems based on the Lighthill–Whitham–Richards model, which explicitly capture vehicle spillback. The DNL describes and predicts the spatial-temporal evolution of traffic flow and congestion on a network that is consistent with established route and departure time choices of travelers. The LWR-based DNL model is first formulated as a system of partial differential algebraic equations. We then investigate the continuous dependence of merge and diverge junction models with respect to their initial/boundary conditions, which leads to the continuity of the path delay operator through the wave-front tracking methodology and the generalized tangent vector technique. As part of our analysis leading up to the main continuity result, we also provide an estimation of the minimum network supply without resort to any numerical computation. In particular, it is shown that gridlock can never occur in a finite time horizon in the DNL model.
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Abstract New computation algorithms for a fluid-dynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more... more
Abstract New computation algorithms for a fluid-dynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more efficient method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new method, namely the Fast Shock Fitting method (FSF), based on good theorical properties of the solution of the problem is introduced.
ABSTRACT
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In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the... more
In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the wavelet domain and then allows to predict wavelet coefficients at each scale from the first one. This property combined with the theoretical re sults
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We consider an hyperbolic conservation law with discontinuous ux. Such partial dieren tial equation arises in dieren t applicative problems, in particular we are motivated by a model of trac o w. We provide a new formulation in terms of... more
We consider an hyperbolic conservation law with discontinuous ux. Such partial dieren tial equation arises in dieren t applicative problems, in particular we are motivated by a model of trac o w. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic
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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 functions, i.e. functions describing... more
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 functions, i.e. functions describing paths for cars. ¶ We propose a definition of solution at junctions, which depends on the traffic-type functions. Finally we prove, for
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ABSTRACT We consider the properties of stability and robustness of an optimal control synthesis obtained for the problem of route tracking by a kinematic vehicle moving forward only with a lower bounded turning radius. This model,... more
ABSTRACT We consider the properties of stability and robustness of an optimal control synthesis obtained for the problem of route tracking by a kinematic vehicle moving forward only with a lower bounded turning radius. This model, sometimes referred to as “Dubins' vehicle”, is relevant to the kinematics of road vehicles as well as aircraft cruising at constant altitude, or sea vessels
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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 consider a network composed by a single... more
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 consider a network composed by a single node $J$ with $n$ incoming and $m$ outgoing arcs. We extend at $J$ the classical Kru\v{z}kov entropy obtaining two conditions, denoted by (E1) and (E2): the first requiring entropy condition for all Kru\v{z}kov entropies, the second only for the value corresponding to sonic point. First we show that in case $n \ne m$, no Riemann solver can satisfy the strongest condition. Then we characterize all the Riemann solvers at $J$ satisfying the strongest condition (E1), in the case of nodes with at most two incoming and two outgoing arcs. Finally we focus three different Riemann solvers, introduced in previous papers. In particular, we show that the Riemann solver introduced for data networks is the only one always satisfying (E2). Comment: 35 pages
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In this paper we present an agent-based model for the simulation of animal groups on the move in two and three dimensions. The model takes into account only two forces: a long-range cohesion and a short-range re- pulsion. We also consider... more
In this paper we present an agent-based model for the simulation of animal groups on the move in two and three dimensions. The model takes into account only two forces: a long-range cohesion and a short-range re- pulsion. We also consider the visual field of the animals and the different zones where cohesion and repulsion are active. Interactions between ani- mals are both metric and topological. Unlike most of the existing models, we do not take into account the alignment of the velocities. The main result is that, despite the simplicity of the model, we can obtain almost all known patterns commonly seen in nature for animal groups (globu- lar, extended and front clusters, columns, Vees, Jays, echelons) without adding extra animal-specific features, disclosing the basic causes of pat- tern formation.
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This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway... more
This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which the observation operator is linear. This article presents a new scalar hyperbolic partial differential equation (PDE) model for traffic velocity evolution on highways, based on the seminal Lighthill-Whitham-Richards (LWR) PDE for density. Equivalence of the solution of the new velocity PDE and the solution of the LWR PDE is shown for quadratic flux functions. Because this equivalence does not hold for general flux functions, a discretized model of velocity evolution based on the Godunov scheme applied to the LWR PDE is proposed. Using an explicit instantiation of the weak boundary conditions of the PDE, the discrete velocity evolution model is generalized to a network, thus making ...
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The aim of this paper is to optimize traffic distribution coefficients in order to maximize the trasmission speed of packets over a network. We consider a macroscopic fluidodynamic model dealing with packets flow proposed in [10], where... more
The aim of this paper is to optimize traffic distribution coefficients in order to maximize the trasmission speed of packets over a network. We consider a macroscopic fluidodynamic model dealing with packets flow proposed in [10], where the dynamics at nodes (routers) is decided by a routing algorithm depending on traffic distribution (and priority) coefficients. We solve completely the problem for the simple case of two incoming and two outgoing lines.
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ABSTRACT
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In this paper, we consider the problem of steering complex dynamical systems among equilibria in their state space in efficient ways. Efficiency is considered as the possibility of compactly representing the (typically very large, or... more
In this paper, we consider the problem of steering complex dynamical systems among equilibria in their state space in efficient ways. Efficiency is considered as the possibility of compactly representing the (typically very large, or infinite) set of reachable equilibria and quickly computing plans to move among them. To this purpose, we consider the possibility of building lattice structures by purposefully introducing quantization of inputs. We consider different ways in which control actions can be encoded in a finite or numerable set of symbols, review different applications where symbolic encoding of control actions can be employed with success, and provide a unified framework in which to study the many different possible manifestations of the idea.
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In this paper we consider the problem of coordination of large number of robots subject to low information constraint. We solve the problem of safe-minimum time control for robots, that are car-like modeled and have different goal... more
In this paper we consider the problem of coordination of large number of robots subject to low information constraint. We solve the problem of safe-minimum time control for robots, that are car-like modeled and have different goal configurations, by designing two different controls: the safe and the time-optimal ones, and by tuning them suitably. We can see the tuning as
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... Ugo Boscain SISSA-ISAS Via Beirut 2-4 34014 Trieste, ITALY, boscainQsissa. ... Generically all extremals are finite con-catenations of regular arcs that are bang or corresponds to a smooth feedback. Moreover the support of ex-tremals... more
... Ugo Boscain SISSA-ISAS Via Beirut 2-4 34014 Trieste, ITALY, boscainQsissa. ... Generically all extremals are finite con-catenations of regular arcs that are bang or corresponds to a smooth feedback. Moreover the support of ex-tremals is a Whitney stratified set. ...
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In this paper we consider the problem of coordination of large number of robots subject to low information constraint. We solve the problem of safe-minimum time control for robots, that are car-like modeled and have different goal... more
In this paper we consider the problem of coordination of large number of robots subject to low information constraint. We solve the problem of safe-minimum time control for robots, that are car-like modeled and have different goal configurations, by designing two different controls: the safe and the time-optimal ones, and by tuning them suitably. We can see the tuning as
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Page 1. Proceedings of the 42nd IEEE Conferenee on Decision and Control Mad, Hawaii USA, December 2003 WeA07-3 Time-optimal control of a swing Jayant E. Kulkarni Department of Theoretical and Applied Mechanics Come11 University Ithaca, NY... more
Page 1. Proceedings of the 42nd IEEE Conferenee on Decision and Control Mad, Hawaii USA, December 2003 WeA07-3 Time-optimal control of a swing Jayant E. Kulkarni Department of Theoretical and Applied Mechanics Come11 University Ithaca, NY 14850, USA. ...
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ABSTRACT We consider a scalar partial differential equation of hyperbolic type in conservation form on a network composed by n incoming and m outgoing arcs, connected together at a node. We deal with the Riemann problem at the node and we... more
ABSTRACT We consider a scalar partial differential equation of hyperbolic type in conservation form on a network composed by n incoming and m outgoing arcs, connected together at a node. We deal with the Riemann problem at the node and we present various Riemann solvers, introduced in the literature, satisfying some general properties, which ensure existence of a solution to a Cauchy problem.
... Antonio Bicchi1, Alessia Marigo2, and Benedetto Piccoli3 ... Although nonholonomic mechanics has a long history, dating back at least to the work of Hertz and Hölder towards the end of the 19th century, it is still today a very active... more
... Antonio Bicchi1, Alessia Marigo2, and Benedetto Piccoli3 ... Although nonholonomic mechanics has a long history, dating back at least to the work of Hertz and Hölder towards the end of the 19th century, it is still today a very active domain of research, both for its theoretical ...
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The aim of this paper is to introduce a macroscopic ∞uid dynamic model dealing with the ∞ows of information on a telecommunication network encoded in packets. Taking an intermediate time and space scale, we propose a model similar to that... more
The aim of this paper is to introduce a macroscopic ∞uid dynamic model dealing with the ∞ows of information on a telecommunication network encoded in packets. Taking an intermediate time and space scale, we propose a model similar to that introduced recently for car tra-c, see (11). For dynamics at nodes we consider two "routing algorithms" and prove existence of
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The ever increasing demands on passengers' comfort, safety, emissions and fuel consumption imposed by car manufacturers and regulations call for robust techniques and the use of cycle-accurate models in automotive control. In this... more
The ever increasing demands on passengers' comfort, safety, emissions and fuel consumption imposed by car manufacturers and regulations call for robust techniques and the use of cycle-accurate models in automotive control. In this paper, we focus on such approach to control the idle speed. It is natural to resort to hybrid methodologies, because of the rich combination of time and
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Recently, significant interest has been raised in the study of hybrid systems. In this paper we analyze the performance of various stabilizers, including discontinuous and hybrid controls, to stabilize two model problems, namely a... more
Recently, significant interest has been raised in the study of hybrid systems. In this paper we analyze the performance of various stabilizers, including discontinuous and hybrid controls, to stabilize two model problems, namely a linearized pendulum with observed position and the Brockett system. In relation to this study we faced the presence of periodic orbits in hybrid stabilizers that are
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A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle. Indeed, due to the vehicles' design and the actuation modes usually under... more
A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle. Indeed, due to the vehicles' design and the actuation modes usually under consideration for underwater plateforms the number of actuator switchings must be kept to a small value to insure feasibility and precision. This is the main objective of the algorithm presented in this paper. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six-degrees-of ...
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ABSTRACT From the text: The present issue of Discrete and Continuous Dynamical Systems - Series S is devoted to traffic modeling and management. This subject dramatically developed in recent years. On one hand, the successes of the... more
ABSTRACT From the text: The present issue of Discrete and Continuous Dynamical Systems - Series S is devoted to traffic modeling and management. This subject dramatically developed in recent years. On one hand, the successes of the analytical theory of conservation laws have provided new tools to traffic researchers while, on the other hand, the requirements coming from the applications have grown dramatically. Remarkably, two of the papers that opened the way to this decades long development date the same year. In 1995 “The Unique Limit of the Glimm Scheme” by A. Bressan [Arch. Ration. Mech. Anal. 103, No. 3, 205–230 (1995; Zbl 0835.35088)] gave a basis for several well posedness results for 1D systems of conservation laws. In the same year, “Requiem for High-Order Fluid Approximations of Traffic Flow” by C. Daganzo [Transp. Res. Part B: Methodol. 29B, No. 4, 277–287 (1995)] posed serious criticisms to models studied at that time and started to fix minimal requirements for a traffic model to be seriously considered.
ABSTRACT Dynamic flux balance analysis of a bioreactor is based on the coupling between a dynamic problem, which models the evolution of biomass, feeding substrates and metabolites, and a linear program, which encodes the metabolic... more
ABSTRACT Dynamic flux balance analysis of a bioreactor is based on the coupling between a dynamic problem, which models the evolution of biomass, feeding substrates and metabolites, and a linear program, which encodes the metabolic activity inside cells. We cast the problem in the language of optimal control and propose a hybrid formulation to model the full coupling between macroscopic and microscopic level. On a given location of the hybrid system we analyze necessary conditions given by the Pontryagin Maximum Principle and discuss the presence of singular arcs. In particular, for the single-input case we prove that optimal controls are bang-bang. For the multi-input case, under suitable assumptions, we prove that generically with respect to initial conditions optimal controls are bang-bang.