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Programme 2012-2013

Organizers: Frédéric Bonnans, Cristopher Hermosilla, Hasnaa Zidani. Place: ENSTA ParisTech or École Polytechnique How to get ENSTA, see http://www.ensta-paristech.fr/en/getting-ensta-paristech

Jun 03, 2013 (Salle de Séminaire, UMA) :

 
  •  14:00  Florence Hubert (Aix-Marseille Université)
Modelisation de la croissance metastatique d'un cancer et des traitements anti-cancereux.

 

Abstract: Le cancer est devenu la première cause de mortalité en France. L'utilisation de modèles mathématiques pour décrire cette maladie ainsi que les traitements administrés semble très prometeuse. Nous verrons dans cet exposé un certain nombre de difficultés auxquelles doivent faire face le médecin et les outils que les mathématiciens peuvent leur apporter.


May 24, 2013 (Salle de Séminaire, UMA) :

 
  •  14:00  Franco Rampazzo (Università degli Studi di Padova, Italy)
(Sup + Bolza)-control problems as dynamic differential games.

 

Abstract: We consider a (L∞+Bolza)-control problem, namely a problem where the payoff is the sum of a sup (actually ess-sup) functional and a classical Bolza functional. Owing to the ⟨L1,L∞⟩ duality, the (L∞+Bolza)-control problem is rephrased in terms of a static differential game, where a new variable k plays the role of a maximizer. In this framework 1 − k is regarded as the available fuel for the maximizer. The relevant (and unusual) fact is that this static game is equivalent to the corresponding dynamic differential game, which allows the (upper) value function to verify a rather simple boundary value problem. 

The whole approach will be hopefully utilized to get necessary conditions for a curve to be a minimizer.

 

 

Past Events:

 

April 22, 2013 (Salle de Séminaire, UMA) :

 
  •  14:00  Alexandre Chapoutot (LIE, ENSTA)
Calcul d'ensemble de trajectoires de systèmes hybrides par des méthodes numériques garanties.

 

Abstract: Cet exposé s'intéresse au problème d'atteignabilité dans les systèmes hybrides, c'est-à-dire aux systèmes composés d'éléments évoluant continûment dans le temps et d'éléments évoluant de manière discrète dans le temps, pour lesquels nous voulons connaître l'ensemble des trajectoires pour un ensemble de conditions initiales. Cette problématique est abordée suivant une vision informaticienne issue du domaine de la vérification formelle. Nous présentons une approche fondée sur  les méthodes d'intégration  numérique garantie pour résoudre des équations différentielles ordinaires et sur l'interpolation polynomiale garantie pour calculer les instants d'apparition d'événements de zero-crosssing. Après avoir présenté le contexte de ce travail, nous aborderons les principales caractéristiques des outils utilisés qui seront illustrés à l'aide d'exemples.

 

  •  15:30  Srinivas Sridharan (UMA, ENSTA)
An overview of scalable control and estimation using max-plus methods.

 

Abstract: Conventional approaches to solving optimal control problems using dynamic programming require the solution of Hamilton Jacobi equations. Numerical solution techniques suffer from the curse of dimensionality and are thus intractable in higher dimensions. This talk will provide a gentle introduction to a promising class of control synthesis methods which are more scalable than grid based methods. Further the application of these 'max-plus' methods to an intriguing range of problems in estimation and control of linear, non-linear and multi-sensor problems will be described.


March 11, 2013 (Salle de Séminaire, UMA) :

 
  •  14:00  Eladio Ocaña (Instituto de Matemática y Ciencias Afines, Lima)
Explicit solution for singular calculus of variations in infinite horizon.

 

Abstract: We consider a one dimensional infinite horizon calculus of variations problem (P), where the integrand is linear with respect to the velocity. The Euler-Lagrange equation, when defined, is not a differential equation as usual, but reduces to an algebraic (or transcendental) equation $C(x)=0 $. Thus this first order optimality condition  is not informative for optimal solutions with initial condition $x_0 $ such that $C(x_0) \neq 0 $. To problem (P) we associate an auxiliary calculus of variations problem whose solutions connect as quickly as possible the initial conditions to some constant solutions. Then we deduce the optimality of these curves, called MRAPs (Most Rapid Approach Path),  for (P). According to the optimality criterium we consider, we have to assume a classical transversality condition. We observe that (P) possesses the Turnpike property, the Turnpike set being given by the preceding particular constant solutions of the auxiliary problem.

 

  • 15:30  Adriano Festa (Imperial College London)

Pursuit-Evasion Games with Multi-Pursuer: a decomposition approach.

 

Abstract: In a pursuit-evasion game, each pursuer attempts to minimize the distance between himself (P) and the evader (E) and capture it in the shortest time, whereas the evader tries to maximize the same distance to escape from being captured. In this talk, we deal with PE games with an evader and n pursuers. It is easy to imagine that the dimension of the space where the agents are moving increases with the number of pursuers, making the problem hard to solve. We will use the well-known PDE approach and an original decomposition technique to get over the big dimensionality contained in the problem. Simulation results will show the effectiveness of the proposed strategy of resolution as well as the limitations of it.

 
 
 

February 19, 2013 (Salle de Séminaire, UMA) :

 
  •  14:00  Bean-San Goh (Curtin University, Sarawak Malaysia)
Optimal control of single species biological population.

  • 15:30  Frédéric Bonnans (Commands & CMAP)

Stabilité des arcs singuliers pour un problème de commande optimale perturbé.


January 7, 2013 (Salle de Séminaire, UMA) :

 
  • 14:00  Kristian Debrabant (University of Southern Denmark)
Convergence of one-step methods for SDEs.

  • 15:30  Fabien Crauste (Université Claude Bernard Lyon 1)

Modélisation de la production des globules rouges : Équations de transport non-linéaires et stabilité.


December 20, 2012 (Salle de Séminaire, UMA) :


  •  14:00 Dusan Stipanovic (University of Illinois at Urbana-Champaign)
Controlling Dynamic Systems with Multiple Objectives.
 

December 10, 2012 (Amphi 2329, UMA) :


  •  14:00 Soutenance de thèse de Giovanni Granato (Commands)
Optimisation de lois de gestion énergétiques des véhicules hybrides.

October 22, 2012 (Salle de Séminaire, UMA) :


  • 14:00  Fabio Ancona (Università degli Studi di Padova, Italy)
On the construction of patchy feedback. A general approach for stabilization and optimization problems.

  • 15:30 Piermarco Cannarsa (Università degli Studi di Roma “Tor Vergata”, Italy)
Role and behaviour of singularities in dynamic programming.
 

October 15, 2012 (Salle de Séminaire, UMA) :


  • 14:00  Internal Meeting of COMMANDS team
 

October 8, 2012 (Salle de Séminaire, UMA) :


  • 14:00  Jong-Shi Pang (University of Illinois at Urbana-Champaign, USA)
A unified numerical method for optimal control problems with mixed state-control constraints.

  • 15:30 Philip Jameson Graber (Commands)
Direct and indirect nonlinear damping mechanisms for the wave equation.



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