--- _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' ...