Global optimization approach for the climbing problem of multi-stage launchers
Résumé
This paper deals with a problem of trajectory optimization of the flight phases of a threestage
launcher. The aim of this optimization problem is to minimize the consumption of
ergols that is need to steer the launcher from the Earth to the GEO. Here we use a global
optimization procedure based on Hamilton-Jacobi-Bellman (HJB) approach. An interesting
by-product of the HJB approach is the synthesis of the optimal control in feedback form.
Once the HJB equation is solved, for any starting point, the reconstruction of the optimal
trajectory can be performed in real time.
We aim at showing that combining several new techniques for the HJB approach we can
obtain efficient solutions to a fully nonlinear control problem. The global optimization
procedure proposed here takes also into account parametric optimisation that appears in the
flight phases.
Several recent advanced numerical techniques for HJB equations (high order finite difference
schemes, parallel computing) are used to solve a 6-dimensional optimal control problem
within a reasonable CPU time.
This work has been carried out in the frame of CNES Launchers’ Research and Technology
program