[{"status":"public","type":"preprint","file_date_updated":"2025-03-11T08:27:32Z","department":[{"_id":"101"}],"user_id":"97359","_id":"58953","project":[{"_id":"106","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","grant_number":"453112019"}],"page":"23","citation":{"ama":"Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. <i>arXiv:250307576</i>. Published online 2025.","chicago":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","ieee":"R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems,” <i>arXiv:2503.07576</i>. 2025.","bibtex":"@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems}, journal={arXiv:2503.07576}, author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }","mla":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","short":"R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).","apa":"Gerlach, R., &#38; von der Gracht, S. (2025). Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. In <i>arXiv:2503.07576</i>."},"has_accepted_license":"1","author":[{"id":"32655","full_name":"Gerlach, Raphael","orcid":"0009-0002-4750-2051","last_name":"Gerlach","first_name":"Raphael"},{"first_name":"Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","id":"97359","full_name":"von der Gracht, Sören"}],"date_updated":"2025-03-11T08:53:02Z","oa":"1","file":[{"date_created":"2025-03-11T08:27:32Z","creator":"svdg","date_updated":"2025-03-11T08:27:32Z","access_level":"open_access","file_name":"Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf","file_id":"58954","file_size":812198,"content_type":"application/pdf","relation":"main_file"}],"abstract":[{"lang":"eng","text":"In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze their collective Fsync dynamics using of equivariant dynamical systems theory. To this end, we show that the corresponding evolution function commutes with rotational and reflective transformations of R^2. These form a group that is isomorphic to O(2) x S_n, the product group of the orthogonal group and the permutation on n elements. The theory of equivariant dynamical systems is used to deduce a hierarchy along which symmetries of a robot swarm can potentially increase following an arbitrary protocol. By decoupling the Look phase from the Compute and Move phases in the mathematical description of an LCM cycle, this hierarchy can be characterized in terms of automorphisms of connectivity graphs. In particular, we find all possible types of symmetry increase, if the decoupled Compute and Move phase is invertible. Finally, we apply our results to protocols which induce state-dependent linear dynamics, where the reduced system consisting of only the Compute and Move phase is linear."}],"publication":"arXiv:2503.07576","language":[{"iso":"eng"}],"keyword":["dynamical systems","coupled systems","distributed computing","robot swarms","autonomous mobile robots","symmetry","equivariant dynamics"],"ddc":["004"],"external_id":{"arxiv":["2503.07576"]},"year":"2025","title":"Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems","date_created":"2025-03-11T08:21:05Z"},{"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"author":[{"first_name":"Radu Ioan","full_name":"Bot, Radu Ioan","last_name":"Bot"},{"first_name":"Konstantin","id":"56399","full_name":"Sonntag, Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496"}],"oa":"1","date_updated":"2025-10-16T11:56:36Z","citation":{"ama":"Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>. Published online 2025.","chicago":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","ieee":"R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).","mla":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","bibtex":"@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}, journal={Journal of Mathematical Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025} }","apa":"Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>."},"has_accepted_license":"1","file_date_updated":"2024-11-28T08:58:00Z","user_id":"56399","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"_id":"57472","status":"public","type":"journal_article","title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","date_created":"2024-11-28T08:58:17Z","year":"2025","language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"external_id":{"arxiv":["2411.18422"]},"file":[{"file_size":4291134,"file_id":"57473","file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf","access_level":"open_access","date_updated":"2024-11-28T08:58:00Z","creator":"sonntagk","date_created":"2024-11-28T08:58:00Z","relation":"main_file","content_type":"application/pdf"}],"abstract":[{"text":"In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.","lang":"eng"}],"publication":"Journal of Mathematical Analysis and Applications"},{"quality_controlled":"1","issue":"12","year":"2022","date_created":"2022-05-05T06:22:55Z","title":"Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems","publication":"14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)","abstract":[{"lang":"eng","text":"While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model. "}],"keyword":["neural networks","physics-guided","data-driven","multi-objective optimization","system identification","machine learning","dynamical systems"],"language":[{"iso":"eng"}],"citation":{"apa":"Schön, O., Götte, R.-S., &#38; Timmermann, J. (2022). Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems. <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>, <i>55</i>(12), 19–24. <a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>","short":"O. Schön, R.-S. Götte, J. Timmermann, in: 14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022), 2022, pp. 19–24.","mla":"Schön, Oliver, et al. “Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems.” <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>, vol. 55, no. 12, 2022, pp. 19–24, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>.","bibtex":"@inproceedings{Schön_Götte_Timmermann_2022, title={Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>}, number={12}, booktitle={14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)}, author={Schön, Oliver and Götte, Ricarda-Samantha and Timmermann, Julia}, year={2022}, pages={19–24} }","ama":"Schön O, Götte R-S, Timmermann J. Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems. In: <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>. Vol 55. ; 2022:19-24. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>","chicago":"Schön, Oliver, Ricarda-Samantha Götte, and Julia Timmermann. “Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems.” In <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>, 55:19–24, 2022. <a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>.","ieee":"O. Schön, R.-S. Götte, and J. Timmermann, “Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems,” in <i>14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)</i>, Casablanca, Morocco, 2022, vol. 55, no. 12, pp. 19–24, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2022.07.282\">https://doi.org/10.1016/j.ifacol.2022.07.282</a>."},"page":"19-24","intvolume":"        55","date_updated":"2024-11-13T08:43:16Z","author":[{"first_name":"Oliver","last_name":"Schön","full_name":"Schön, Oliver"},{"first_name":"Ricarda-Samantha","id":"43992","full_name":"Götte, Ricarda-Samantha","last_name":"Götte"},{"first_name":"Julia","last_name":"Timmermann","full_name":"Timmermann, Julia","id":"15402"}],"volume":55,"conference":{"name":"14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)","start_date":"2022-06-29","end_date":"2022-07-01","location":"Casablanca, Morocco"},"doi":"https://doi.org/10.1016/j.ifacol.2022.07.282","type":"conference","status":"public","_id":"31066","user_id":"43992","department":[{"_id":"153"},{"_id":"880"}]}]