On the Refinement of Discretization for Optimal Control Problems

Abstract

In the framework of future launchers design studies, CNES and ONERA are studying possible improvements of tools and methods for trajectory optimization. Trajectory optimization of reusable launch vehicle (RLV) is a very complex task calling for a versatile tool, which should be able to address - either simultaneously or separately - ascent and reentry trajectory phases. Improvement can be made in comparison with existing methods and tools regarding issues such as the global processing of ascent and reentry phases, or specific constraints of reentry phases. In this context, a first candidate for a new optimization method is currently being studied. This method is an adapted interior point algorithm, associated with a Runge-Kutta discretization scheme of the optimal control problem. In this paper we will focus on the presentation of the RK method to use, the error estimation and the mesh refinement policy to use in order to have an optimal complexity and then a fast algorithm.