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Rauert. “Funnel Cruise Control.” Automatica, vol. 119, 109061, 2020.","bibtex":"@article{Berger_Rauert_2020, title={Funnel cruise control}, volume={119}, number={109061}, journal={Automatica}, author={Berger, Thomas and Rauert, A.-L.}, year={2020} }"},"year":"2020","type":"journal_article"},{"series_title":"Differential-Algebraic Equations Forum","type":"book_chapter","citation":{"ama":"Berger T, Huy Hoang L, Reis T. Vector relative degree and funnel control for differential-algebraic systems. In: Grundel S, Reis T, Schöps S, eds. Progress in Differential-Algebraic Equations II. Differential-Algebraic Equations Forum. Springer; 2020:213-255.","apa":"Berger, T., Huy Hoang, L., & Reis, T. (2020). Vector relative degree and funnel control for differential-algebraic systems. In S. Grundel, T. Reis, & S. Schöps (Eds.), Progress in Differential-Algebraic Equations II (pp. 213–255). Springer.","chicago":"Berger, Thomas, Le Huy Hoang, and T. Reis. “Vector Relative Degree and Funnel Control for Differential-Algebraic Systems.” In Progress in Differential-Algebraic Equations II, edited by S. Grundel, T. Reis, and S. Schöps, 213–55. Differential-Algebraic Equations Forum. Springer, 2020.","mla":"Berger, Thomas, et al. “Vector Relative Degree and Funnel Control for Differential-Algebraic Systems.” Progress in Differential-Algebraic Equations II, edited by S. Grundel et al., Springer, 2020, pp. 213–55.","bibtex":"@inbook{Berger_Huy Hoang_Reis_2020, series={Differential-Algebraic Equations Forum}, title={Vector relative degree and funnel control for differential-algebraic systems}, booktitle={Progress in Differential-Algebraic Equations II}, publisher={Springer}, author={Berger, Thomas and Huy Hoang, Le and Reis, T.}, editor={Grundel, S. and Reis, T. and Schöps, S.}, year={2020}, pages={213–255}, collection={Differential-Algebraic Equations Forum} }","short":"T. Berger, L. Huy Hoang, T. Reis, in: S. Grundel, T. Reis, S. 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Cham: Springer International Publishing, 2020. https://doi.org/10.1007/978-3-030-58653-9_22.","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","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.","short":"C. Balsa, O. Cots, J. Gergaud, B.E. Wembe Moafo, in: Lecture Notes in Electrical Engineering, Springer International Publishing, Cham, 2020."}},{"publication_status":"published","publication_identifier":{"issn":["1292-8119","1262-3377"]},"title":"A Zermelo navigation problem with a vortex singularity","language":[{"iso":"eng"}],"doi":"10.1051/cocv/2020058","date_updated":"2023-01-16T12:09:22Z","date_created":"2022-10-24T12:51:05Z","status":"public","volume":27,"publication":"ESAIM: Control, Optimisation and Calculus of Variations","keyword":["Computational Mathematics","Control and Optimization","Control and Systems Engineering"],"author":[{"last_name":"Bonnard","full_name":"Bonnard, Bernard","first_name":"Bernard"},{"last_name":"Cots","first_name":"Olivier","full_name":"Cots, Olivier"},{"full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","id":"95394","last_name":"Wembe Moafo"}],"publisher":"EDP Sciences","user_id":"95394","abstract":[{"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.","lang":"eng"}],"type":"journal_article","year":"2020","citation":{"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.","short":"B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and Calculus of Variations 27 (2020).","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} }","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.","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.","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","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"},"article_number":"S10","_id":"33866","intvolume":" 27"}]