Numerical schemes for first order Hamilton-Jacobi-Bellman equations.
Application to a problem of atmospheric re-entry

Proposition type:
Latest date:
june, 2007
Numerical scheme, HJB equation, viscosity solution, Optimal control, atmospheric re-entry problem, state constraints
Our team is seeking to recruit a postdoctoral research assistant for working on the developement of numerical methods for first order HJB equations coming from optimal control problems of ODE's with state constraints. For such problems, the value function (solution of an HJB equation) is discontinuous, and the set of discontinuities represents the border of the whole of the admissible trajectories. The discretization of the HJB equation provides an approximation of the value function. However, monotone schemes will provide a poor approximation quality because of numerical diffusion, in particular around the discontinuities.
Recent works in the team, on numerical methods in dimension 1, prove that it is possible to build a non-monotone scheme wich gives a good approximation of the discontinuous value function. We would like to generalize this result for dimension d>1.

A second part of this work will concern the reconstruction of the optimal trajectories, from the computed value function.

The whole of the study is motivated by an industrial application. More precisely, we aim at using the HJB approach to solve a time optimal control problem of atmospheric re-entry of a space shuttle, under constraints of heat flux and load factor.
The numerical methods developed and studied (during this post doc) will be tested on a real model provided by the CNES (French Space Agency).

Applications including a full curriculum vitae, a list of publications, and the names and addresses of at least two referees should be sent to Contacts : Hasnaa Zidani or Frédéric Bonnans

Required skills: Capacities in scientific computation ./