[{"language":[{"iso":"eng"}],"_id":"59792","department":[{"_id":"636"}],"user_id":"87909","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic> we extend the <jats:italic>exponential turnpike property</jats:italic> to the <jats:italic>exponential trim turnpike</jats:italic> for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem.\r\n</jats:p>"}],"status":"public","publication":"Mathematics of Control, Signals, and Systems","type":"journal_article","title":"Trim turnpikes for optimal control problems with symmetries","doi":"10.1007/s00498-025-00408-w","date_updated":"2025-05-05T09:24:09Z","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Kathrin","full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp"},{"first_name":"Sofya","last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"date_created":"2025-05-05T09:23:38Z","year":"2025","citation":{"short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","bibtex":"@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim turnpikes for optimal control problems with symmetries}, DOI={<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }","mla":"Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","apa":"Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025). Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>","ieee":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","chicago":"Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, 2025. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>.","ama":"Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>"},"publication_identifier":{"issn":["0932-4194","1435-568X"]},"publication_status":"published"},{"external_id":{"arxiv":["2502.05123"]},"_id":"58544","user_id":"85279","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"language":[{"iso":"eng"}],"type":"preprint","abstract":[{"text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. ","lang":"eng"}],"status":"public","date_updated":"2025-02-10T08:36:12Z","oa":"1","date_created":"2025-02-10T08:26:45Z","author":[{"first_name":"Denis","id":"98502","full_name":"Kopylov, Denis","last_name":"Kopylov"},{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"first_name":"Laura","full_name":"Ares, Laura","last_name":"Ares"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"orcid":"0000-0001-8864-2072","last_name":"Meier","full_name":"Meier, Torsten","id":"344","first_name":"Torsten"},{"first_name":"Polina","last_name":"Sharapova","full_name":"Sharapova, Polina","id":"60286"},{"orcid":"0000-0002-5844-3205","last_name":"Sperling","id":"75127","full_name":"Sperling, Jan","first_name":"Jan"}],"title":"Multiphoton, multimode state classification for nonlinear optical circuits ","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.05123","open_access":"1"}],"publication_status":"submitted","year":"2025","citation":{"mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>.","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits .","chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” ."}},{"date_created":"2025-05-05T09:25:28Z","author":[{"last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279","first_name":"Christian"},{"last_name":"Singh","full_name":"Singh, Pranav","first_name":"Pranav"},{"first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394","full_name":"Wembe Moafo, Boris Edgar"}],"date_updated":"2025-09-30T15:16:09Z","title":"Adaptive higher order reversible integrators for memory efficient deep learning","has_accepted_license":"1","citation":{"ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025.","ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025.","apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>.","bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025."},"year":"2025","user_id":"85279","department":[{"_id":"636"}],"external_id":{"arxiv":["2410.09537"]},"_id":"59794","language":[{"iso":"eng"}],"file_date_updated":"2025-05-05T09:28:02Z","ddc":["510"],"type":"preprint","file":[{"date_updated":"2025-05-05T09:28:02Z","date_created":"2025-05-05T09:28:02Z","creator":"sofyam","file_size":1830758,"access_level":"closed","file_id":"59795","file_name":"2410.09537v2.pdf","content_type":"application/pdf","success":1,"relation":"main_file"}],"status":"public","abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}]},{"user_id":"16199","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"project":[{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"name":"TRR 142 - Project Area C","_id":"56"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"_id":"62980","language":[{"iso":"eng"}],"article_number":"033062","type":"journal_article","publication":"Physical Review Research","status":"public","abstract":[{"lang":"eng","text":"<jats:p>We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.</jats:p>"}],"date_created":"2025-12-09T09:08:39Z","author":[{"first_name":"Denis A.","last_name":"Kopylov","full_name":"Kopylov, Denis A."},{"first_name":"Christian","id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"first_name":"Laura","full_name":"Ares, Laura","last_name":"Ares"},{"full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier","full_name":"Meier, Torsten","id":"344"},{"full_name":"Sharapova, Polina R.","id":"60286","last_name":"Sharapova","first_name":"Polina R."},{"first_name":"Jan","orcid":"0000-0002-5844-3205","last_name":"Sperling","id":"75127","full_name":"Sperling, Jan"}],"volume":7,"publisher":"American Physical Society (APS)","date_updated":"2025-12-09T09:10:01Z","doi":"10.1103/sv6z-v1gk","title":"Multiphoton, multimode state classification for nonlinear optical circuits","issue":"3","publication_status":"published","publication_identifier":{"issn":["2643-1564"]},"citation":{"ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>","ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).","mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>"},"intvolume":"         7","year":"2025"},{"year":"2025","citation":{"chicago":"Meier, Torsten, Polina R. Sharapova, Jan Sperling, Sina Ober-Blöbaum, Boris Edgar Wembe Moafo, and Christian Offen. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits,” 2025.","ieee":"T. Meier, P. R. Sharapova, J. Sperling, S. Ober-Blöbaum, B. E. Wembe Moafo, and C. Offen, “Multiphoton, multimode state classification for nonlinear optical circuits.” 2025.","ama":"Meier T, Sharapova PR, Sperling J, Ober-Blöbaum S, Wembe Moafo BE, Offen C. Multiphoton, multimode state classification for nonlinear optical circuits. Published online 2025.","short":"T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo, C. Offen, (2025).","mla":"Meier, Torsten, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits</i>. 2025.","bibtex":"@article{Meier_Sharapova_Sperling_Ober-Blöbaum_Wembe Moafo_Offen_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, author={Meier, Torsten and Sharapova, Polina R. and Sperling, Jan and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar and Offen, Christian}, year={2025} }","apa":"Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B. E., &#38; Offen, C. (2025). <i>Multiphoton, multimode state classification for nonlinear optical circuits</i>."},"date_updated":"2025-12-09T09:10:23Z","date_created":"2025-12-09T08:59:27Z","author":[{"first_name":"Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier","full_name":"Meier, Torsten","id":"344"},{"first_name":"Polina R.","full_name":"Sharapova, Polina R.","id":"60286","last_name":"Sharapova"},{"first_name":"Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","full_name":"Sperling, Jan","id":"75127"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo"},{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen"}],"title":"Multiphoton, multimode state classification for nonlinear optical circuits","type":"preprint","abstract":[{"lang":"eng","text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes."}],"status":"public","_id":"62979","project":[{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"_id":"56","name":"TRR 142 - Project Area C"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"},{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"department":[{"_id":"15"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"230"},{"_id":"623"},{"_id":"429"},{"_id":"35"}],"user_id":"16199","language":[{"iso":"eng"}]},{"publication_status":"submitted","issue":"15","year":"2025","citation":{"ama":"Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free Cayley methods. <i>J Comput Appl Math</i>. 477(15). doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>","chicago":"Wembe Moafo, Boris Edgar, Cristian  Offen, Sofya Maslovskaya, Sina Ober-Blöbaum, and Pranav Singh. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i> 477, no. 15 (n.d.). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>.","ieee":"B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh, “Commutator-free Cayley methods,” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi: <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","apa":"Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., &#38; Singh, P. (n.d.). Commutator-free Cayley methods. <i>J. Comput. Appl. Math</i>, <i>477</i>(15). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>","short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","mla":"Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","bibtex":"@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free Cayley methods}, volume={477}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>}, number={15}, journal={J. Comput. Appl. Math}, author={Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav} }"},"intvolume":"       477","date_updated":"2025-12-16T15:17:27Z","date_created":"2025-04-10T14:42:52Z","author":[{"full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"first_name":"Cristian ","full_name":"Offen, Cristian ","last_name":"Offen"},{"first_name":"Sofya","full_name":"Maslovskaya, Sofya","id":"87909","last_name":"Maslovskaya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Singh","full_name":"Singh, Pranav","first_name":"Pranav"}],"volume":477,"title":"Commutator-free Cayley methods","doi":"10.1016/j.cam.2025.117184","type":"journal_article","publication":"J. Comput. Appl. Math","abstract":[{"text":"Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators.","lang":"eng"}],"status":"public","_id":"59507","user_id":"95394","department":[{"_id":"94"}],"language":[{"iso":"eng"}]},{"publication":"Mathematical Control and Related Fields","type":"journal_article","status":"public","_id":"35206","user_id":"95394","keyword":["Applied Mathematics","Control and Optimization","General Medicine"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2156-8472","2156-8499"]},"publication_status":"published","issue":"0","year":"2022","page":"0-0","citation":{"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} }","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>.","short":"B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related Fields 0 (2022) 0–0.","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>","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>.","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>."},"date_updated":"2023-01-16T12:07:51Z","publisher":"American Institute of Mathematical Sciences (AIMS)","volume":"0","author":[{"first_name":"Bernard","full_name":"Bonnard, Bernard","last_name":"Bonnard"},{"full_name":"Rouot, Jérémy","last_name":"Rouot","first_name":"Jérémy"},{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"}],"date_created":"2023-01-04T10:26:56Z","title":"Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies","doi":"10.3934/mcrf.2022052"},{"publication_identifier":{"issn":["0167-6911"]},"publication_status":"published","intvolume":"       161","citation":{"apa":"Bonnard, B., Cots, O., Gergaud, J., &#38; 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. <i>Systems &#38;amp; Control Letters</i>, <i>161</i>, Article 105140. <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">https://doi.org/10.1016/j.sysconle.2022.105140</a>","short":"B. Bonnard, O. Cots, J. Gergaud, B.E. Wembe Moafo, Systems &#38;amp; Control Letters 161 (2022).","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.” <i>Systems &#38;amp; Control Letters</i>, vol. 161, 105140, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>.","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={<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>}, number={105140}, journal={Systems &#38;amp; Control Letters}, publisher={Elsevier BV}, author={Bonnard, B. and Cots, O. and Gergaud, J. and Wembe Moafo, Boris Edgar}, year={2022} }","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. <i>Systems &#38;amp; Control Letters</i>. 2022;161. doi:<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>","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.” <i>Systems &#38;amp; Control Letters</i> 161 (2022). <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">https://doi.org/10.1016/j.sysconle.2022.105140</a>.","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,” <i>Systems &#38;amp; Control Letters</i>, vol. 161, Art. no. 105140, 2022, doi: <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>."},"year":"2022","volume":161,"author":[{"full_name":"Bonnard, B.","last_name":"Bonnard","first_name":"B."},{"first_name":"O.","full_name":"Cots, O.","last_name":"Cots"},{"full_name":"Gergaud, J.","last_name":"Gergaud","first_name":"J."},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"date_created":"2022-10-24T12:54:24Z","publisher":"Elsevier BV","date_updated":"2023-01-16T12:08:58Z","doi":"10.1016/j.sysconle.2022.105140","title":"Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls","publication":"Systems &amp; Control Letters","type":"journal_article","status":"public","user_id":"95394","_id":"33869","language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Mechanical Engineering","General Computer Science","Control and Systems Engineering"],"article_number":"105140"},{"keyword":["Immunology"],"language":[{"iso":"eng"}],"_id":"33871","user_id":"95394","abstract":[{"lang":"eng","text":"<jats:p>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.</jats:p>"}],"status":"public","type":"journal_article","publication":"ESAIM: Proceedings and Surveys","title":"Homotopic approach for turnpike and singularly perturbed optimal control problems","doi":"10.1051/proc/202171105","date_updated":"2023-01-16T12:08:28Z","publisher":"EDP Sciences","author":[{"last_name":"Cots","full_name":"Cots, Olivier","first_name":"Olivier"},{"first_name":"Joseph","full_name":"Gergaud, Joseph","last_name":"Gergaud"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"date_created":"2022-10-24T13:00:10Z","volume":71,"year":"2021","citation":{"ieee":"O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Homotopic approach for turnpike and singularly perturbed optimal control problems,” <i>ESAIM: Proceedings and Surveys</i>, vol. 71, pp. 43–53, 2021, doi: <a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>.","chicago":"Cots, Olivier, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Homotopic Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” <i>ESAIM: Proceedings and Surveys</i> 71 (2021): 43–53. <a href=\"https://doi.org/10.1051/proc/202171105\">https://doi.org/10.1051/proc/202171105</a>.","ama":"Cots O, Gergaud J, Wembe Moafo BE. Homotopic approach for turnpike and singularly perturbed optimal control problems. <i>ESAIM: Proceedings and Surveys</i>. 2021;71:43-53. doi:<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>","mla":"Cots, Olivier, et al. “Homotopic Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” <i>ESAIM: Proceedings and Surveys</i>, vol. 71, EDP Sciences, 2021, pp. 43–53, doi:<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>.","short":"O. Cots, J. Gergaud, B.E. Wembe Moafo, ESAIM: Proceedings and Surveys 71 (2021) 43–53.","bibtex":"@article{Cots_Gergaud_Wembe Moafo_2021, title={Homotopic approach for turnpike and singularly perturbed optimal control problems}, volume={71}, DOI={<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>}, journal={ESAIM: Proceedings and Surveys}, publisher={EDP Sciences}, author={Cots, Olivier and Gergaud, Joseph and Wembe Moafo, Boris Edgar}, year={2021}, pages={43–53} }","apa":"Cots, O., Gergaud, J., &#38; Wembe Moafo, B. E. (2021). Homotopic approach for turnpike and singularly perturbed optimal control problems. <i>ESAIM: Proceedings and Surveys</i>, <i>71</i>, 43–53. <a href=\"https://doi.org/10.1051/proc/202171105\">https://doi.org/10.1051/proc/202171105</a>"},"page":"43-53","intvolume":"        71","publication_status":"published","publication_identifier":{"issn":["2267-3059"]}},{"year":"2021","citation":{"short":"B.E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications, n.d.","bibtex":"@book{Wembe Moafo, title={Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications}, author={Wembe Moafo, Boris Edgar} }","mla":"Wembe Moafo, Boris Edgar. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>.","apa":"Wembe Moafo, B. E. (n.d.). <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>.","ieee":"B. E. Wembe Moafo, <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>. .","chicago":"Wembe Moafo, Boris Edgar. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>, n.d.","ama":"Wembe Moafo BE. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>."},"page":"180","publication_status":"submitted","has_accepted_license":"1","related_material":{"link":[{"url":"https://hal.archives-ouvertes.fr/tel-03601394v2","relation":"confirmation"}]},"title":"Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications","date_updated":"2023-01-16T12:09:11Z","oa":"1","author":[{"full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"date_created":"2022-10-25T09:08:05Z","file":[{"file_size":6662644,"file_id":"33873","access_level":"open_access","file_name":"These_Hal.pdf","date_updated":"2022-10-25T09:07:57Z","creator":"wboris","date_created":"2022-10-25T09:07:57Z","relation":"main_file","content_type":"application/pdf"}],"status":"public","type":"dissertation","ddc":["510"],"file_date_updated":"2022-10-25T09:07:57Z","language":[{"iso":"fre"}],"extern":"1","_id":"33872","user_id":"95394"},{"doi":"10.1007/978-3-030-58653-9_22","title":"Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow","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","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"date_created":"2022-10-24T12:59:19Z","publisher":"Springer International Publishing","date_updated":"2023-01-16T12:08:44Z","citation":{"bibtex":"@inbook{Balsa_Cots_Gergaud_Wembe Moafo_2020, place={Cham}, title={Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>}, 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} }","mla":"Balsa, Carlos, et al. “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.” <i>Lecture Notes in Electrical Engineering</i>, Springer International Publishing, 2020, doi:<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>.","short":"C. Balsa, O. Cots, J. Gergaud, B.E. Wembe Moafo, in: Lecture Notes in Electrical Engineering, Springer International Publishing, Cham, 2020.","apa":"Balsa, C., Cots, O., Gergaud, J., &#38; Wembe Moafo, B. E. (2020). Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow. In <i>Lecture Notes in Electrical Engineering</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">https://doi.org/10.1007/978-3-030-58653-9_22</a>","chicago":"Balsa, Carlos, Olivier Cots, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.” In <i>Lecture Notes in Electrical Engineering</i>. Cham: Springer International Publishing, 2020. <a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">https://doi.org/10.1007/978-3-030-58653-9_22</a>.","ieee":"C. Balsa, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow,” in <i>Lecture Notes in Electrical Engineering</i>, Cham: Springer International Publishing, 2020.","ama":"Balsa C, Cots O, Gergaud J, Wembe Moafo BE. Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow. In: <i>Lecture Notes in Electrical Engineering</i>. Springer International Publishing; 2020. doi:<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>"},"place":"Cham","year":"2020","publication_status":"published","publication_identifier":{"issn":["1876-1100","1876-1119"],"isbn":["9783030586522","9783030586539"]},"language":[{"iso":"eng"}],"user_id":"95394","_id":"33870","status":"public","type":"book_chapter","publication":"Lecture Notes in Electrical Engineering"},{"citation":{"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>","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>.","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>.","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>.","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>"},"intvolume":"        27","year":"2020","publication_status":"published","publication_identifier":{"issn":["1292-8119","1262-3377"]},"doi":"10.1051/cocv/2020058","title":"A Zermelo navigation problem with a vortex singularity","date_created":"2022-10-24T12:51:05Z","author":[{"first_name":"Bernard","full_name":"Bonnard, Bernard","last_name":"Bonnard"},{"full_name":"Cots, Olivier","last_name":"Cots","first_name":"Olivier"},{"full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"volume":27,"date_updated":"2023-01-16T12:09:22Z","publisher":"EDP Sciences","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>"}],"type":"journal_article","publication":"ESAIM: Control, Optimisation and Calculus of Variations","language":[{"iso":"eng"}],"article_number":"S10","keyword":["Computational Mathematics","Control and Optimization","Control and Systems Engineering"],"user_id":"95394","_id":"33866"}]