---
_id: '35206'
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Jérémy
full_name: Rouot, Jérémy
last_name: Rouot
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics
in optimal control illustrated by two case studies. Mathematical Control and
Related Fields. 2022;0(0):0-0. doi:10.3934/mcrf.2022052
apa: Bonnard, B., Rouot, J., & Wembe Moafo, B. E. (2022). Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies. Mathematical
Control and Related Fields, 0(0), 0–0. https://doi.org/10.3934/mcrf.2022052
bibtex: '@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies}, volume={0},
DOI={10.3934/mcrf.2022052},
number={0}, journal={Mathematical Control and Related Fields}, publisher={American
Institute of Mathematical Sciences (AIMS)}, author={Bonnard, Bernard and Rouot,
Jérémy and Wembe Moafo, Boris Edgar}, year={2022}, pages={0–0} }'
chicago: 'Bonnard, Bernard, Jérémy Rouot, and Boris Edgar Wembe Moafo. “Accessibility
Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.”
Mathematical Control and Related Fields 0, no. 0 (2022): 0–0. https://doi.org/10.3934/mcrf.2022052.'
ieee: 'B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of
abnormal geodesics in optimal control illustrated by two case studies,” Mathematical
Control and Related Fields, vol. 0, no. 0, pp. 0–0, 2022, doi: 10.3934/mcrf.2022052.'
mla: Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in
Optimal Control Illustrated by Two Case Studies.” Mathematical Control and
Related Fields, vol. 0, no. 0, American Institute of Mathematical Sciences
(AIMS), 2022, pp. 0–0, doi:10.3934/mcrf.2022052.
short: B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related
Fields 0 (2022) 0–0.
date_created: 2023-01-04T10:26:56Z
date_updated: 2023-01-16T12:07:51Z
doi: 10.3934/mcrf.2022052
issue: '0'
keyword:
- Applied Mathematics
- Control and Optimization
- General Medicine
language:
- iso: eng
page: 0-0
publication: Mathematical Control and Related Fields
publication_identifier:
issn:
- 2156-8472
- 2156-8499
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Accessibility properties of abnormal geodesics in optimal control illustrated
by two case studies
type: journal_article
user_id: '95394'
volume: '0'
year: '2022'
...
---
_id: '33869'
article_number: '105140'
author:
- first_name: B.
full_name: Bonnard, B.
last_name: Bonnard
- first_name: O.
full_name: Cots, O.
last_name: Cots
- first_name: J.
full_name: Gergaud, J.
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Bonnard B, Cots O, Gergaud J, Wembe Moafo BE. Abnormal geodesics in 2D-Zermelo
navigation problems in the case of revolution and the fan shape of the small time
balls. Systems & Control Letters. 2022;161. doi:10.1016/j.sysconle.2022.105140
apa: Bonnard, B., Cots, O., Gergaud, J., & Wembe Moafo, B. E. (2022). Abnormal
geodesics in 2D-Zermelo navigation problems in the case of revolution and the
fan shape of the small time balls. Systems & Control Letters, 161,
Article 105140. https://doi.org/10.1016/j.sysconle.2022.105140
bibtex: '@article{Bonnard_Cots_Gergaud_Wembe Moafo_2022, title={Abnormal geodesics
in 2D-Zermelo navigation problems in the case of revolution and the fan shape
of the small time balls}, volume={161}, DOI={10.1016/j.sysconle.2022.105140},
number={105140}, journal={Systems & Control Letters}, publisher={Elsevier
BV}, author={Bonnard, B. and Cots, O. and Gergaud, J. and Wembe Moafo, Boris Edgar},
year={2022} }'
chicago: Bonnard, B., O. Cots, J. Gergaud, and Boris Edgar Wembe Moafo. “Abnormal
Geodesics in 2D-Zermelo Navigation Problems in the Case of Revolution and the
Fan Shape of the Small Time Balls.” Systems & Control Letters 161
(2022). https://doi.org/10.1016/j.sysconle.2022.105140.
ieee: 'B. Bonnard, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Abnormal geodesics
in 2D-Zermelo navigation problems in the case of revolution and the fan shape
of the small time balls,” Systems & Control Letters, vol. 161,
Art. no. 105140, 2022, doi: 10.1016/j.sysconle.2022.105140.'
mla: Bonnard, B., et al. “Abnormal Geodesics in 2D-Zermelo Navigation Problems in
the Case of Revolution and the Fan Shape of the Small Time Balls.” Systems
& Control Letters, vol. 161, 105140, Elsevier BV, 2022, doi:10.1016/j.sysconle.2022.105140.
short: B. Bonnard, O. Cots, J. Gergaud, B.E. Wembe Moafo, Systems & Control
Letters 161 (2022).
date_created: 2022-10-24T12:54:24Z
date_updated: 2023-01-16T12:08:58Z
doi: 10.1016/j.sysconle.2022.105140
intvolume: ' 161'
keyword:
- Electrical and Electronic Engineering
- Mechanical Engineering
- General Computer Science
- Control and Systems Engineering
language:
- iso: eng
publication: Systems & Control Letters
publication_identifier:
issn:
- 0167-6911
publication_status: published
publisher: Elsevier BV
status: public
title: Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution
and the fan shape of the small time balls
type: journal_article
user_id: '95394'
volume: 161
year: '2022'
...
---
_id: '33871'
abstract:
- lang: eng
text: 'The first aim of this article is to present the link between the
turnpike property and the singular perturbations theory: the first one being a
particular case of the second one. Then, thanks to this link, we set up a new
framework based on continuation methods for the resolution of singularly perturbed
optimal control problems. We consider first the turnpike case, then, we generalize
the approach to general control problems with singular perturbations (that is
with fast but also slow variables). We illustrate each step with an example.'
author:
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Joseph
full_name: Gergaud, Joseph
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Cots O, Gergaud J, Wembe Moafo BE. Homotopic approach for turnpike and singularly
perturbed optimal control problems. ESAIM: Proceedings and Surveys. 2021;71:43-53.
doi:10.1051/proc/202171105'
apa: 'Cots, O., Gergaud, J., & Wembe Moafo, B. E. (2021). Homotopic approach
for turnpike and singularly perturbed optimal control problems. ESAIM: Proceedings
and Surveys, 71, 43–53. https://doi.org/10.1051/proc/202171105'
bibtex: '@article{Cots_Gergaud_Wembe Moafo_2021, title={Homotopic approach for turnpike
and singularly perturbed optimal control problems}, volume={71}, DOI={10.1051/proc/202171105},
journal={ESAIM: Proceedings and Surveys}, publisher={EDP Sciences}, author={Cots,
Olivier and Gergaud, Joseph and Wembe Moafo, Boris Edgar}, year={2021}, pages={43–53}
}'
chicago: 'Cots, Olivier, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Homotopic
Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” ESAIM:
Proceedings and Surveys 71 (2021): 43–53. https://doi.org/10.1051/proc/202171105.'
ieee: 'O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Homotopic approach for turnpike
and singularly perturbed optimal control problems,” ESAIM: Proceedings and
Surveys, vol. 71, pp. 43–53, 2021, doi: 10.1051/proc/202171105.'
mla: 'Cots, Olivier, et al. “Homotopic Approach for Turnpike and Singularly Perturbed
Optimal Control Problems.” ESAIM: Proceedings and Surveys, vol. 71, EDP
Sciences, 2021, pp. 43–53, doi:10.1051/proc/202171105.'
short: 'O. Cots, J. Gergaud, B.E. Wembe Moafo, ESAIM: Proceedings and Surveys 71
(2021) 43–53.'
date_created: 2022-10-24T13:00:10Z
date_updated: 2023-01-16T12:08:28Z
doi: 10.1051/proc/202171105
intvolume: ' 71'
keyword:
- Immunology
language:
- iso: eng
page: 43-53
publication: 'ESAIM: Proceedings and Surveys'
publication_identifier:
issn:
- 2267-3059
publication_status: published
publisher: EDP Sciences
status: public
title: Homotopic approach for turnpike and singularly perturbed optimal control problems
type: journal_article
user_id: '95394'
volume: 71
year: '2021'
...
---
_id: '33872'
author:
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Wembe Moafo BE. Geometric and Numerical Methods in Optimal Control and Zermelo
Problems on Revolution Surfaces - Applications.
apa: Wembe Moafo, B. E. (n.d.). Geometric and Numerical Methods in Optimal Control
and Zermelo Problems on Revolution Surfaces - Applications.
bibtex: '@book{Wembe Moafo, title={Geometric and Numerical Methods in Optimal Control
and Zermelo Problems on Revolution Surfaces - Applications}, author={Wembe Moafo,
Boris Edgar} }'
chicago: Wembe Moafo, Boris Edgar. Geometric and Numerical Methods in Optimal
Control and Zermelo Problems on Revolution Surfaces - Applications, n.d.
ieee: B. E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and
Zermelo Problems on Revolution Surfaces - Applications. .
mla: Wembe Moafo, Boris Edgar. Geometric and Numerical Methods in Optimal Control
and Zermelo Problems on Revolution Surfaces - Applications.
short: B.E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and
Zermelo Problems on Revolution Surfaces - Applications, n.d.
date_created: 2022-10-25T09:08:05Z
date_updated: 2023-01-16T12:09:11Z
ddc:
- '510'
extern: '1'
file:
- access_level: open_access
content_type: application/pdf
creator: wboris
date_created: 2022-10-25T09:07:57Z
date_updated: 2022-10-25T09:07:57Z
file_id: '33873'
file_name: These_Hal.pdf
file_size: 6662644
relation: main_file
file_date_updated: 2022-10-25T09:07:57Z
has_accepted_license: '1'
language:
- iso: fre
oa: '1'
page: '180'
publication_status: submitted
related_material:
link:
- relation: confirmation
url: https://hal.archives-ouvertes.fr/tel-03601394v2
status: public
title: Geometric and Numerical Methods in Optimal Control and Zermelo Problems on
Revolution Surfaces - Applications
type: dissertation
user_id: '95394'
year: '2021'
...
---
_id: '33870'
author:
- first_name: Carlos
full_name: Balsa, Carlos
last_name: Balsa
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Joseph
full_name: Gergaud, Joseph
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Balsa C, Cots O, Gergaud J, Wembe Moafo BE. Minimum Energy Control of Passive
Tracers Advection in Point Vortices Flow. In: Lecture Notes in Electrical Engineering.
Springer International Publishing; 2020. doi:10.1007/978-3-030-58653-9_22'
apa: Balsa, C., Cots, O., Gergaud, J., & Wembe Moafo, B. E. (2020). Minimum
Energy Control of Passive Tracers Advection in Point Vortices Flow. In Lecture
Notes in Electrical Engineering. Springer International Publishing. https://doi.org/10.1007/978-3-030-58653-9_22
bibtex: '@inbook{Balsa_Cots_Gergaud_Wembe Moafo_2020, place={Cham}, title={Minimum
Energy Control of Passive Tracers Advection in Point Vortices Flow}, DOI={10.1007/978-3-030-58653-9_22},
booktitle={Lecture Notes in Electrical Engineering}, publisher={Springer International
Publishing}, author={Balsa, Carlos and Cots, Olivier and Gergaud, Joseph and Wembe
Moafo, Boris Edgar}, year={2020} }'
chicago: 'Balsa, Carlos, Olivier Cots, Joseph Gergaud, and Boris Edgar Wembe Moafo.
“Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.”
In Lecture Notes in Electrical Engineering. Cham: Springer International
Publishing, 2020. https://doi.org/10.1007/978-3-030-58653-9_22.'
ieee: 'C. Balsa, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Minimum Energy Control
of Passive Tracers Advection in Point Vortices Flow,” in Lecture Notes in Electrical
Engineering, Cham: Springer International Publishing, 2020.'
mla: Balsa, Carlos, et al. “Minimum Energy Control of Passive Tracers Advection
in Point Vortices Flow.” Lecture Notes in Electrical Engineering, Springer
International Publishing, 2020, doi:10.1007/978-3-030-58653-9_22.
short: 'C. Balsa, O. Cots, J. Gergaud, B.E. Wembe Moafo, in: Lecture Notes in Electrical
Engineering, Springer International Publishing, Cham, 2020.'
date_created: 2022-10-24T12:59:19Z
date_updated: 2023-01-16T12:08:44Z
doi: 10.1007/978-3-030-58653-9_22
language:
- iso: eng
place: Cham
publication: Lecture Notes in Electrical Engineering
publication_identifier:
isbn:
- '9783030586522'
- '9783030586539'
issn:
- 1876-1100
- 1876-1119
publication_status: published
publisher: Springer International Publishing
status: public
title: Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow
type: book_chapter
user_id: '95394'
year: '2020'
...
---
_id: '33866'
abstract:
- lang: eng
text: Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible
fluid in the plane define a dynamics with singularities and this leads to a Zermelo
navigation problem describing the ship travel in such a field where the control
is the heading angle. Considering one vortex, we define a time minimization problem
which can be analyzed with the technics of geometric optimal control combined
with numerical simulations, the geometric frame being the extension of Randers
metrics in the punctured plane, with rotational symmetry. Candidates as minimizers
are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions
of a Hamiltonian vector field. We analyze the time minimal solution to transfer
the ship between two points where during the transfer the ship can be either in
a strong current region in the vicinity of the vortex or in a weak current region.
The analysis is based on a micro-local classification of the extremals using mainly
the integrability properties of the dynamics due to the rotational symmetry. The
discussion is complex and related to the existence of an isolated extremal (Reeb)
circle due to the vortex singularity. The explicit computation of cut points where
the extremal curves cease to be optimal is given and the spheres are described
in the case where at the initial point the current is weak.
article_number: S10
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Bonnard B, Cots O, Wembe Moafo BE. A Zermelo navigation problem with a vortex
singularity. ESAIM: Control, Optimisation and Calculus of Variations. 2020;27.
doi:10.1051/cocv/2020058'
apa: 'Bonnard, B., Cots, O., & Wembe Moafo, B. E. (2020). A Zermelo navigation
problem with a vortex singularity. ESAIM: Control, Optimisation and Calculus
of Variations, 27, Article S10. https://doi.org/10.1051/cocv/2020058'
bibtex: '@article{Bonnard_Cots_Wembe Moafo_2020, title={A Zermelo navigation problem
with a vortex singularity}, volume={27}, DOI={10.1051/cocv/2020058},
number={S10}, journal={ESAIM: Control, Optimisation and Calculus of Variations},
publisher={EDP Sciences}, author={Bonnard, Bernard and Cots, Olivier and Wembe
Moafo, Boris Edgar}, year={2020} }'
chicago: 'Bonnard, Bernard, Olivier Cots, and Boris Edgar Wembe Moafo. “A Zermelo
Navigation Problem with a Vortex Singularity.” ESAIM: Control, Optimisation
and Calculus of Variations 27 (2020). https://doi.org/10.1051/cocv/2020058.'
ieee: 'B. Bonnard, O. Cots, and B. E. Wembe Moafo, “A Zermelo navigation problem
with a vortex singularity,” ESAIM: Control, Optimisation and Calculus of Variations,
vol. 27, Art. no. S10, 2020, doi: 10.1051/cocv/2020058.'
mla: 'Bonnard, Bernard, et al. “A Zermelo Navigation Problem with a Vortex Singularity.”
ESAIM: Control, Optimisation and Calculus of Variations, vol. 27, S10,
EDP Sciences, 2020, doi:10.1051/cocv/2020058.'
short: 'B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and
Calculus of Variations 27 (2020).'
date_created: 2022-10-24T12:51:05Z
date_updated: 2023-01-16T12:09:22Z
doi: 10.1051/cocv/2020058
intvolume: ' 27'
keyword:
- Computational Mathematics
- Control and Optimization
- Control and Systems Engineering
language:
- iso: eng
publication: 'ESAIM: Control, Optimisation and Calculus of Variations'
publication_identifier:
issn:
- 1292-8119
- 1262-3377
publication_status: published
publisher: EDP Sciences
status: public
title: A Zermelo navigation problem with a vortex singularity
type: journal_article
user_id: '95394'
volume: 27
year: '2020'
...