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.
Keywords: Hamilton-Jacobi approach, state constraints, maximum running cost, trajectory reconstruction, aircraft landing in windshear
Assellaou, Mohamed 1 ; Bokanowski, Olivier 1 ; Desilles, Anya 1 ; Zidani, Hasnaa 1
@article{M2AN_2018__52_1_305_0,
author = {Assellaou, Mohamed and Bokanowski, Olivier and Desilles, Anya and Zidani, Hasnaa},
title = {Value function and optimal trajectories for a maximum running cost control problem with state constraints. {Application} to an abort landing problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {305--335},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {1},
doi = {10.1051/m2an/2017064},
mrnumber = {3808162},
zbl = {1397.49038},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2017064/}
}
TY - JOUR AU - Assellaou, Mohamed AU - Bokanowski, Olivier AU - Desilles, Anya AU - Zidani, Hasnaa TI - Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 305 EP - 335 VL - 52 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2017064/ DO - 10.1051/m2an/2017064 LA - en ID - M2AN_2018__52_1_305_0 ER -
%0 Journal Article %A Assellaou, Mohamed %A Bokanowski, Olivier %A Desilles, Anya %A Zidani, Hasnaa %T Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 305-335 %V 52 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2017064/ %R 10.1051/m2an/2017064 %G en %F M2AN_2018__52_1_305_0
Assellaou, Mohamed; Bokanowski, Olivier; Desilles, Anya; Zidani, Hasnaa. Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 305-335. doi: 10.1051/m2an/2017064
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