| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 99 | |
| Number of page(s) | 33 | |
| DOI | https://doi.org/10.1051/cocv/2020023 | |
| Published online | 10 December 2020 | |
Singular extremals in L1-optimal control problems: sufficient optimality conditions*
1
Université de Toulon, Aix Marseille Univ, CNRS, LIS,
Marseille, France.
2
DiMaI, Università di Firenze,
50139
Firenze, Italy.
** Corresponding author: francesca-carlotta.chittaro@univ-tln.fr
Received:
10
September
2019
Accepted:
23
April
2020
In this paper we are concerned with generalised L1-minimisation problems, i.e. Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of extremals given by the concatenation of bang, singular and inactive (zero) arcs. The sufficiency of such conditions is proved by means of Hamiltonian methods. As a by-product of the result, we provide an explicit invariant formula for the second variation along the singular arc.
Mathematics Subject Classification: 49J15 / 49J30 / 49K30
Key words: Sufficient optimality conditions / control-affine systems / singular control / L1 minimisation / minimum fuel problem
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.