[{"publication_identifier":{"issn":["0926-6003","1573-2894"]},"publication_status":"published","year":"2024","citation":{"ama":"Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>","ieee":"B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” <i>Computational Optimization and Applications</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","chicago":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, 2024. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>.","apa":"Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. <i>Computational Optimization and Applications</i>. <a href=\"https://doi.org/10.1007/s10589-024-00552-0\">https://doi.org/10.1007/s10589-024-00552-0</a>","mla":"Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>.","short":"B. Gebken, Computational Optimization and Applications (2024).","bibtex":"@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={<a href=\"https://doi.org/10.1007/s10589-024-00552-0\">10.1007/s10589-024-00552-0</a>}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }"},"date_updated":"2024-02-08T08:05:54Z","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"}],"date_created":"2024-02-07T07:23:23Z","title":"A note on the convergence of deterministic gradient sampling in nonsmooth optimization","doi":"10.1007/s10589-024-00552-0","publication":"Computational Optimization and Applications","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.</jats:p>","lang":"eng"}],"status":"public","_id":"51208","department":[{"_id":"101"}],"user_id":"32643","keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization"],"language":[{"iso":"eng"}]},{"title":"Heteroclinic dynamics in network dynamical systems with higher-order interactions","date_created":"2024-03-22T09:04:57Z","publisher":"Oxford University Press (OUP)","year":"2024","issue":"2","language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Applied Mathematics","Computational Mathematics","Control and Optimization","Management Science and Operations Research","Computer Networks and Communications"],"external_id":{"arxiv":["2309.02006"]},"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_id":"52728","access_level":"closed","file_name":"heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf","file_size":649155,"creator":"svdg","date_created":"2024-03-22T09:06:07Z","date_updated":"2024-03-22T09:06:07Z"}],"abstract":[{"lang":"eng","text":"Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures."}],"publication":"Journal of Complex Networks","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf"}],"doi":"10.1093/comnet/cnae009","author":[{"first_name":"Christian","full_name":"Bick, Christian","last_name":"Bick"},{"first_name":"Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","full_name":"von der Gracht, Sören","id":"97359"}],"volume":12,"oa":"1","date_updated":"2024-03-22T09:11:53Z","citation":{"ieee":"C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” <i>Journal of Complex Networks</i>, vol. 12, no. 2, 2024, doi: <a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>.","chicago":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i> 12, no. 2 (2024). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>.","ama":"Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>. 2024;12(2). doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>","apa":"Bick, C., &#38; von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>, <i>12</i>(2). <a href=\"https://doi.org/10.1093/comnet/cnae009\">https://doi.org/10.1093/comnet/cnae009</a>","short":"C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).","bibtex":"@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }","mla":"Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:<a href=\"https://doi.org/10.1093/comnet/cnae009\">10.1093/comnet/cnae009</a>."},"intvolume":"        12","publication_status":"published","publication_identifier":{"issn":["2051-1329"]},"has_accepted_license":"1","file_date_updated":"2024-03-22T09:06:07Z","article_type":"original","user_id":"97359","department":[{"_id":"101"}],"_id":"52726","status":"public","type":"journal_article"},{"keyword":["Applied Mathematics","Control and Optimization","Modeling and Simulation"],"language":[{"iso":"eng"}],"_id":"53317","user_id":"31496","status":"public","type":"journal_article","publication":"Evolution Equations and Control Theory","title":"Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities","doi":"10.3934/eect.2023031","publisher":"American Institute of Mathematical Sciences (AIMS)","date_updated":"2024-04-07T12:36:17Z","date_created":"2024-04-07T12:30:25Z","author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":12,"year":"2023","citation":{"apa":"Tao, Y., &#38; Winkler, M. (2023). Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. <i>Evolution Equations and Control Theory</i>, <i>12</i>(6), 1676–1687. <a href=\"https://doi.org/10.3934/eect.2023031\">https://doi.org/10.3934/eect.2023031</a>","bibtex":"@article{Tao_Winkler_2023, title={Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}, volume={12}, DOI={<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>}, number={6}, journal={Evolution Equations and Control Theory}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler, Michael}, year={2023}, pages={1676–1687} }","mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” <i>Evolution Equations and Control Theory</i>, vol. 12, no. 6, American Institute of Mathematical Sciences (AIMS), 2023, pp. 1676–87, doi:<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>.","short":"Y. Tao, M. Winkler, Evolution Equations and Control Theory 12 (2023) 1676–1687.","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Three-Dimensional Cross-Diffusive SIS Epidemic Model with Saturated Taxis at Large Densities.” <i>Evolution Equations and Control Theory</i> 12, no. 6 (2023): 1676–87. <a href=\"https://doi.org/10.3934/eect.2023031\">https://doi.org/10.3934/eect.2023031</a>.","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities,” <i>Evolution Equations and Control Theory</i>, vol. 12, no. 6, pp. 1676–1687, 2023, doi: <a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>.","ama":"Tao Y, Winkler M. Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities. <i>Evolution Equations and Control Theory</i>. 2023;12(6):1676-1687. doi:<a href=\"https://doi.org/10.3934/eect.2023031\">10.3934/eect.2023031</a>"},"page":"1676-1687","intvolume":"        12","publication_status":"published","publication_identifier":{"issn":["2163-2480"]},"issue":"6"},{"doi":"10.1007/s10957-022-02023-0","title":"Turnpike Property in Optimal Microbial Metabolite Production","author":[{"first_name":"Jean-Baptiste","full_name":"Caillau, Jean-Baptiste","last_name":"Caillau"},{"first_name":"Walid","full_name":"Djema, Walid","last_name":"Djema"},{"first_name":"Jean-Luc","last_name":"Gouzé","full_name":"Gouzé, Jean-Luc"},{"full_name":"Maslovskaya, Sofya","id":"87909","last_name":"Maslovskaya","first_name":"Sofya"},{"full_name":"Pomet, Jean-Baptiste","last_name":"Pomet","first_name":"Jean-Baptiste"}],"date_created":"2022-04-08T17:23:13Z","publisher":"Springer Science and Business Media LLC","date_updated":"2022-04-08T18:23:02Z","citation":{"ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization Theory and Applications</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, 2022. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>.","ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022} }"},"year":"2022","publication_status":"published","publication_identifier":{"issn":["0022-3239","1573-2878"]},"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"user_id":"87909","department":[{"_id":"636"}],"_id":"30861","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>"}],"type":"journal_article","publication":"Journal of Optimization Theory and Applications"},{"user_id":"95394","_id":"35206","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Control and Optimization","General Medicine"],"publication":"Mathematical Control and Related Fields","type":"journal_article","status":"public","volume":"0","date_created":"2023-01-04T10:26:56Z","author":[{"last_name":"Bonnard","full_name":"Bonnard, Bernard","first_name":"Bernard"},{"first_name":"Jérémy","full_name":"Rouot, Jérémy","last_name":"Rouot"},{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"}],"date_updated":"2023-01-16T12:07:51Z","publisher":"American Institute of Mathematical Sciences (AIMS)","doi":"10.3934/mcrf.2022052","title":"Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies","issue":"0","publication_identifier":{"issn":["2156-8472","2156-8499"]},"publication_status":"published","page":"0-0","citation":{"ama":"Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. <i>Mathematical Control and Related Fields</i>. 2022;0(0):0-0. doi:<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>","apa":"Bonnard, B., Rouot, J., &#38; Wembe Moafo, B. E. (2022). Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. <i>Mathematical Control and Related Fields</i>, <i>0</i>(0), 0–0. <a href=\"https://doi.org/10.3934/mcrf.2022052\">https://doi.org/10.3934/mcrf.2022052</a>","bibtex":"@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies}, volume={0}, DOI={<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>}, 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} }","short":"B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related Fields 0 (2022) 0–0.","mla":"Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” <i>Mathematical Control and Related Fields</i>, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2022, pp. 0–0, doi:<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>.","ieee":"B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies,” <i>Mathematical Control and Related Fields</i>, vol. 0, no. 0, pp. 0–0, 2022, doi: <a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>.","chicago":"Bonnard, Bernard, Jérémy Rouot, and Boris Edgar Wembe Moafo. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” <i>Mathematical Control and Related Fields</i> 0, no. 0 (2022): 0–0. <a href=\"https://doi.org/10.3934/mcrf.2022052\">https://doi.org/10.3934/mcrf.2022052</a>."},"year":"2022"},{"publication_identifier":{"issn":["1996-1073"]},"publication_status":"published","issue":"14","year":"2022","intvolume":"        15","citation":{"chicago":"Philipo, Godiana Hagile, Josephine Nakato Kakande, and Stefan Krauter. “Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping.” <i>Energies</i> 15, no. 14 (2022). <a href=\"https://doi.org/10.3390/en15145215\">https://doi.org/10.3390/en15145215</a>.","ieee":"G. H. Philipo, J. N. Kakande, and S. Krauter, “Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping,” <i>Energies</i>, vol. 15, no. 14, Art. no. 5215, 2022, doi: <a href=\"https://doi.org/10.3390/en15145215\">10.3390/en15145215</a>.","ama":"Philipo GH, Kakande JN, Krauter S. Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping. <i>Energies</i>. 2022;15(14). doi:<a href=\"https://doi.org/10.3390/en15145215\">10.3390/en15145215</a>","short":"G.H. Philipo, J.N. Kakande, S. Krauter, Energies 15 (2022).","mla":"Philipo, Godiana Hagile, et al. “Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping.” <i>Energies</i>, vol. 15, no. 14, 5215, MDPI AG, 2022, doi:<a href=\"https://doi.org/10.3390/en15145215\">10.3390/en15145215</a>.","bibtex":"@article{Philipo_Kakande_Krauter_2022, title={Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping}, volume={15}, DOI={<a href=\"https://doi.org/10.3390/en15145215\">10.3390/en15145215</a>}, number={145215}, journal={Energies}, publisher={MDPI AG}, author={Philipo, Godiana Hagile and Kakande, Josephine Nakato and Krauter, Stefan}, year={2022} }","apa":"Philipo, G. H., Kakande, J. N., &#38; Krauter, S. (2022). Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping. <i>Energies</i>, <i>15</i>(14), Article 5215. <a href=\"https://doi.org/10.3390/en15145215\">https://doi.org/10.3390/en15145215</a>"},"date_updated":"2024-10-17T08:46:23Z","publisher":"MDPI AG","volume":15,"date_created":"2023-10-11T08:13:13Z","author":[{"first_name":"Godiana Hagile","full_name":"Philipo, Godiana Hagile","id":"88505","last_name":"Philipo"},{"first_name":"Josephine Nakato","last_name":"Kakande","full_name":"Kakande, Josephine Nakato","id":"88649"},{"id":"28836","full_name":"Krauter, Stefan","last_name":"Krauter","orcid":"0000-0002-3594-260X","first_name":"Stefan"}],"title":"Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping","doi":"10.3390/en15145215","publication":"Energies","type":"journal_article","abstract":[{"lang":"eng","text":"<jats:p>Due to failures or even the absence of an electricity grid, microgrid systems are becoming popular solutions for electrifying African rural communities. However, they are heavily stressed and complex to control due to their intermittency and demand growth. Demand side management (DSM) serves as an option to increase the level of flexibility on the demand side by scheduling users’ consumption patterns profiles in response to supply. This paper proposes a demand-side management strategy based on load shifting and peak clipping. The proposed approach was modelled in a MATLAB/Simulink R2021a environment and was optimized using the artificial neural network (ANN) algorithm. Simulations were carried out to test the model’s efficacy in a stand-alone PV-battery microgrid in East Africa. The proposed algorithm reduces the peak demand, smoothing the load profile to the desired level, and improves the system’s peak to average ratio (PAR). The presence of deferrable loads has been considered to bring more flexible demand-side management. Results promise decreases in peak demand and peak to average ratio of about 31.2% and 7.5% through peak clipping. In addition, load shifting promises more flexibility to customers.</jats:p>"}],"status":"public","_id":"47961","department":[{"_id":"53"}],"user_id":"16148","keyword":["Energy (miscellaneous)","Energy Engineering and Power Technology","Renewable Energy","Sustainability and the Environment","Electrical and Electronic Engineering","Control and Optimization","Engineering (miscellaneous)","Building and Construction"],"article_number":"5215","language":[{"iso":"eng"}]},{"status":"public","abstract":[{"lang":"eng","text":"<jats:p>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.</jats:p>"}],"publication":"ESAIM: Control, Optimisation and Calculus of Variations","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Control and Optimization","Control and Systems Engineering"],"article_number":"S10","user_id":"95394","_id":"33866","intvolume":"        27","citation":{"chicago":"Bonnard, Bernard, Olivier Cots, and Boris Edgar Wembe Moafo. “A Zermelo Navigation Problem with a Vortex Singularity.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i> 27 (2020). <a href=\"https://doi.org/10.1051/cocv/2020058\">https://doi.org/10.1051/cocv/2020058</a>.","ieee":"B. Bonnard, O. Cots, and B. E. Wembe Moafo, “A Zermelo navigation problem with a vortex singularity,” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, vol. 27, Art. no. S10, 2020, doi: <a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>.","ama":"Bonnard B, Cots O, Wembe Moafo BE. A Zermelo navigation problem with a vortex singularity. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>. 2020;27. doi:<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>","apa":"Bonnard, B., Cots, O., &#38; Wembe Moafo, B. E. (2020). A Zermelo navigation problem with a vortex singularity. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, <i>27</i>, Article S10. <a href=\"https://doi.org/10.1051/cocv/2020058\">https://doi.org/10.1051/cocv/2020058</a>","bibtex":"@article{Bonnard_Cots_Wembe Moafo_2020, title={A Zermelo navigation problem with a vortex singularity}, volume={27}, DOI={<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>}, 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} }","short":"B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and Calculus of Variations 27 (2020).","mla":"Bonnard, Bernard, et al. “A Zermelo Navigation Problem with a Vortex Singularity.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, vol. 27, S10, EDP Sciences, 2020, doi:<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>."},"year":"2020","publication_identifier":{"issn":["1292-8119","1262-3377"]},"publication_status":"published","doi":"10.1051/cocv/2020058","title":"A Zermelo navigation problem with a vortex singularity","volume":27,"date_created":"2022-10-24T12:51:05Z","author":[{"first_name":"Bernard","full_name":"Bonnard, Bernard","last_name":"Bonnard"},{"first_name":"Olivier","last_name":"Cots","full_name":"Cots, Olivier"},{"first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"date_updated":"2023-01-16T12:09:22Z","publisher":"EDP Sciences"}]