| Issue |
ESAIM: M2AN
Volume 52, Number 1, January–February 2018
|
|
|---|---|---|
| Page(s) | 305 - 335 | |
| DOI | https://doi.org/10.1051/m2an/2017064 | |
| Published online | 28 May 2018 | |
Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem★
1
Unité de Mathématiques Appliquées (UMA), Ensta ParisTech,
828 Bd des Maréchaux,
91762
Palaiseau Cedex, France
2
University Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS,
75205
Paris, France
* Corresponding author: hasnaa.zidani@ensta-paristech.fr
Received:
6
March
2017
Accepted:
26
December
2017
The aim of this article is to study the Hamilton Jacobi Bellman (HJB) approach for state-constrained control problems with maximum cost. In particular, we are interested in the characterization of the value functions of such problems and the analysis of the associated optimal trajectories, without assuming any controllability assumption. The rigorous theoretical results lead to several trajectory reconstruction procedures for which convergence results are also investigated. An application to a five-state aircraft abort landing problem is then considered, for which several numerical simulations are performed to analyse the relevance of the theoretical approach.
Mathematics Subject Classification: 49L20 / 49M30 / 65M06
Key words: Hamilton-Jacobi approach / state constraints / maximum running cost / trajectory reconstruction / aircraft landing in windshear
© EDP Sciences, SMAI 2018
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