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Contrôle optimal et robuste de l'attitude d'un lanceur. Aspects théoriques et numériques

Antoine Olivier 1, 2
2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : The first objective of this work is to study some aspects of the attitude control problem of a rigid body, in order to optimize the trajectory of a launcher during a ballistic flight. We state this problem in a general mathematical setting, as an optimal control problem with intermediate constraints on the state. Meanwhile, we also implement an optimization software that relies on the combination of a direct method and of an interior-point algorithm to optimize any given ballistic flight, with any number of intermediate constraints, corresponding to any number of satellite separations. Besides, we applied the so-called indirect methods, exploiting Pontryagin maximum principle, to the resolution of this optimal control problem. In this work, optimal trajectories with respect to the consumption are looked after, which corresponds to a L1 cost. Known to be numerically challenging, this criterion can be reached by performing a continuation procedure, starting from a L2 cost, for which it is easier to provide a good initialization of the underlying optimization algorithm. We shall also study other examples of applications for continuation procedures. Eventually, we will present a robust control algorithm, allowing to reach a target point from a perturbed initial point, following a nominal trajectory while preserving its bang-bang structure. The robustness of a control can be improved introducing needle-like variations, and a criterion to measure the robustness of a trajectory is designed, involving the singular value decomposition of some end-point mapping.
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Antoine Olivier. Contrôle optimal et robuste de l'attitude d'un lanceur. Aspects théoriques et numériques. Optimisation et contrôle [math.OC]. Sorbonne Université, 2018. Français. ⟨tel-01962542⟩

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