Publications

2007

• Asymptotic expansion of the optimal control under logarithmic penalty: worked example and open problems
  
  • Alvarez Felipe
  • Bonnans J. Frederic
  • Laurent-Varin Julien
  , 2007. We discuss the problem of expansion of optimal control, state and costate when a logarithmic penalty is applied to constraints. We show that, in a simple case, that the variation of (a regular) junction point, and of the optimal control, state and costate is of order $\eps\log \eps$, where $\eps$ is the penalty parameter.
• A strictly hyperbolic equilibrium phase transition model
  
  • Allaire Grégoire
  • Faccanoni Gloria
  • Kokh Samuel
  Comptes Rendus de l'Academie des Sciences. Série IV, Physique, Astronomie, Elsevier, 2007, 344, pp.135-140. This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a uid. The proof is valid for a very wide class of uids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a de nite negative Hessian matrix for each phase entropy as a function of the speci c volume and internal energy. (10.1016/j.crma.2006.11.008)
  DOI : 10.1016/j.crma.2006.11.008
• The Korteweg-de Vries equation with multiplicative homogeneous noise
  
  • de Bouard Anne
  • Debussche Arnaud
  , 2007, pp.113-133.
• Using switching detection and variational equations for the shooting method
  
  • Martinon Pierre
  • Gergaud Joseph
  Optimal Control Applications and Methods, Wiley, 2007, 28 (2), pp.95-116. We study in this paper the resolution by single shooting of an optimal control problem with a bang-bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright c 2000 John Wiley & Sons, Ltd.
• Global weak solutions to a ferrofluid flow model
  
  • Amirat Youcef
  • Hamdache Kamel
  Mathematical Methods in the Applied Sciences, Wiley, 2007, 31 (2), pp.123-151.