Publications

2018

• Continuous Optimal Control Approaches to Microgrid Energy Management
  
  • Heymann Benjamin
  • Bonnans J. Frederic
  • Martinon Pierre
  • Silva Francisco
  • Lanas Fernando
  • Jimenez Guillermo
  Energy Systems, Springer, 2018, 9 (1), pp.59-77. —We propose a novel method for the microgrid energy management problem by introducing a continuous-time, rolling horizon formulation. The energy management problem is formulated as a deterministic optimal control problem (OCP). We solve (OCP) with two classical approaches: the direct method [1], and Bellman's Dynamic Programming Principle (DPP) [2]. In both cases we use the optimal control toolbox BOCOP [3] for the numerical simulations. For the DPP approach we implement a semi-Lagrangian scheme [4] adapted to handle the optimization of switching times for the on/off modes of the diesel generator. The DPP approach allows for an accurate modeling and is computationally cheap. It finds the global optimum in less than 3 seconds, a CPU time similar to the Mixed Integer Linear Programming (MILP) approach used in [5]. We achieve this performance by introducing a trick based on the Pontryagin Maximum Principle (PMP). The trick increases the computation speed by several orders and also improves the precision of the solution. For validation purposes, simulation are performed using datasets from an actual isolated microgrid located in northern Chile. Results show that DPP method is very well suited for this type of problem when compared with the MILP approach.
• Gauge-reversing maps on cones, and Hilbert and Thompson isometries
  
  • Walsh Cormac
  Geometry and Topology, Mathematical Sciences Publishers, 2018, 22 (1), pp.55-104. We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone. (10.2140/gt.2018.22.55)
  DOI : 10.2140/gt.2018.22.55
• Linearized Navier-Stokes Equations for Aeroacoustics using Stabilized Finite Elements: Boundary Conditions and Industrial Application to Aft-Fan Noise Propagation
  
  • Bissuel Aloïs
  • Allaire Grégoire
  • Daumas Laurent
  • Barré Sébastien
  • Rey Floriane
  Computers and Fluids, Elsevier, 2018. In this paper, a numerical method for solving the linearized Navier-Stokes equations is presented for aeroacoustic sound propagation problem. The Navier-Stokes equations are linearized in the frequency domain. The fan noise of jet engine is emitted nearly selectively at certain frequencies, which depend on the rotation velocity of the fan. A frequency domain approach is highly suitable for this kind of problem, instead of a costly time-dependent simulation which can handle a large range of frequencies depending on the time step and the mesh. The calculations presented here were all made using Aether, a Navier-Stokes code which uses finite elements stabilized with SUPG (Streamline Upwind Galerkin). Automatic code differentiation was used to linearize this code. Entropy variables bring interesting mathematical properties to the numerical scheme, but also prevent the easy implementation of boundary conditions. For instance, the pressure is a non-linear combination of the entropy variables. Imposing a pressure variation needs a linearization of this relation which is detailed herein. The performance of different types of boundary conditions used to impose the acoustic pressure variation inside the engine is studied in detail. Finally, a very surprising effect of the SUPG scheme was to transform a homogeneous Dirichlet boundary condition on all variables to a transparent one which is able to let only outgoing waves pass * Dassault Aviation 78, quai Marcel 1 through with no incoming wave. A one-dimensional toy model is given to explain how SUPG brings about this transformation. The last part of the article is dedicated to an industrial test case. The geometry of a model turbine from the Clean Sky European project was used for sound propagation of the fan exhaust noise of a jet engine. Computations on several modes with increasing complexities were done and the results compared to a boundary element method which served as a reference when no mean flow is present. Results of a computation with a mean flow are shown.
• On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds
  
  • Sacchelli Ludovic
  • Sigalotti Mario
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2018. In this article we study the validity of the Whitney $C^1$ extension property for horizontal curves in sub-Riemannian manifolds endowed with 1-jets that satisfy a first-order Taylor expansion compatibility condition. We first consider the equiregular case, where we show that the extension property holds true whenever a suitable non-singularity property holds for the input-output maps on the Carnot groups obtained by nilpotent approximation. We then discuss the case of sub-Riemannian manifolds with singular points and we show that all step-2 manifolds satisfy the $C^1$ extension property. We conclude by showing that the $C^1$ extension property implies a Lusin-like approximation theorem for horizontal curves on sub-Riemannian manifolds.
• Avis en réponse à la saisine HCB - dossier 2018-150. Paris, le 24 octobre 2018
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2018.