About Dynamical Systems Appearing in the Microscopic Traffic Modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue may be introduced, and the ergodic theory may be used to define a growth rate under additional technical assumptions. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of two roads with one junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions. To simulate these systems, we have to compute their dynamics, which are not quite simple. For building them in a modular way, we introduce generalized parallel, series and feedback compositions of piecewise linear concave dynamics.Comment: PDF 38 page

METANET : a system for network problems study

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The Dynamic Equations of the Tree Morphogenesis GreenLab Model

We explicit the dynamic equations followed by a tree during its growth according to the Greenlab model. In a first part we explicit the Organogenesis equations. In the second part, we recall the equations which, using a macroscopic photosynthesis point of view, describe with a great precision the evolution of the organ sizes. In a third part we establish the morphogenesis equations describing the geometry of a tree. The three parts are illustrated with an example

Optimisation de la gestion d'une maison chauffée par le soleil et une pompe à chaleur

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Identification aveugle de structure propre sous excitation non-stationnaire

L'identification aveugle de la structure propre d'un système linéaire multivariable est effectuée par une méthode sous-espace appliquée aux matrices de covariances des seuls signaux de sortie, les entrées étant inconnues et non-stationnaires. L'analyse des vibrations est un exemple important de problèmes réels pouvant être posés et résolus de cette manière. Le traitement conjoint de signaux enregistrés à des moments différents, et sous excitations différentes, est un problème crucial dans ce domaine. La méthode sous-espace proposée pour résoudre ce problème de fusion est, comme la méthode classique, basée essentiellement sur une propriété de factorisation de la matrice de Hankel (et des covariances des sorties) du système. Des résultats expérimentaux illustrent les performances de la méthode. L'utilisation pour l'exploitation des données de vols d'essai d'avions est discutée

Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are uniquely defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue is introduced, and the ergodic theory is used to define a growth rate. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the average growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of roads with a junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions

In-flight structural identification:input/output versus output-only data processing

The problem of in-flight data analysis, for the purpose of structural model identification under both measured and uncontrolled non-stationary excitation, is addressed. Input/output and output-only eigenstructure identification methods are described and compared, within two classes of methods: subspace-based and prediction error. In particular, different types of relevant projections for handling the known (measured) and unknown (uncontrolled) inputs are discussed. The relevance of the methods is emphasized through numerical results obtained on flight test data sets