Publications

2007

• 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.
• Leçons de mathématiques d'aujourd'hui. Vol. 3
  
  • Perthame Benoît
  • Rauch Jeffrey
  • El Karoui Nicole
  • Yor Marc
  • Werner Wendelin
  • Viennot Xavier
  • Teissier Bernard
  • Cerveau Dominique
  • Morel Fabien
  • Berthelot Pierre
  • Kahn Bruno
  • Lafforgue Laurent
  , 2007, pp.xx-426.
• Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints
  
  • Bonnans Frédéric J.
  • Hermant Audrey
  , 2007. This paper deals with the optimal control problem of an ordinary differential equation with several pure state constraints, of arbitrary orders, as well as mixed control-state constraints. We assume (i) the Hamiltonian to be strongly convex and the mixed constraints to be convex w.r.t. the control variable, and (ii) a linear independence condition of the active constraints at their respective order to hold. We give a complete analysis of the smoothness and junction conditions of the control and of the constraints multipliers. This allow us to obtain, when there are finitely many nontangential junction points, a theory of no-gap second-order optimality conditions and a characterization of the well-posedness of the shooting algorithm. These results generalize those obtained in the case of a scalar-valued state constraint and a scalar-valued control.