Hamilton-Jacobi-Bellman approach for the climbing problem for multi-stage launchers


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Abstract : This study aims to investigate the Hamilton-Jacobi-Bellman (HJB) approach for solving an optimization problem for space launchers. We consider a simplified (realistic) flight mission of the European launcher Ariane 5 to the GTO orbit, and aim to minimize the fuel consumption.We consider the complete flight including stage separations and dynamic pressure constraint.Numerical experiments are performed with data by CNES (French space agency)and show the relevance of our approach.By using an anti-diffusive scheme, we obtain in small CPU time the backward reachable set and the optimal trajectory.Comparisons with a reference trajectory of CNES are presented.

Mots Clés: Multi-stage launchers; Trajectory optimization; Minimum time problem; Hamilton-Jacobi-Bellman approach