Hamilton-jacobi-bellman Approach for the Climbing Problem for Multi-stage Launchers

In this paper we investigate the Hamilton-Jacobi-Bellman (HJB) approach for solving a complex real-world optimal control problem in high dimension. We consider the climbing problem for the European launcher Ariane V: The launcher has to reach the Geostationary Transfer Orbit with minimal propellant consumption under state/control constraints. In order to circumvent the well-known curse of dimensionality, we reduce the number of variables in the model exploiting the specific features concerning the dynamics of the mass. This generates a non–standard optimal control problem formulation. We show that the joint employment of the most advanced mathematical techniques for the numerical solution of HJB equations allows one to achieve practicable results in reasonable time.