{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-stability-analysis-of-optimal-state","title":"On the stability analysis of deep neural network representations of an optimal state-feedback","arxiv_id":"1812.02532","date":"2018-12-06","proceeding":null,"authors":["Dario Izzo","Dharmesh Tailor","Thomas Vasileiou"],"abstract":"Recent work have shown how the optimal state-feedback, obtained as the\nsolution to the Hamilton-Jacobi-Bellman equations, can be approximated for\nseveral nonlinear, deterministic systems by deep neural networks. When\nimitation (supervised) learning is used to train the neural network on optimal\nstate-action pairs, for instance as derived by applying Pontryagin's theory of\noptimal processes, the resulting model is referred here as the guidance and\ncontrol network. In this work, we analyze the stability of nonlinear and\ndeterministic systems controlled by such networks. We then propose a method\nutilising differential algebraic techniques and high-order Taylor maps to gain\ninformation on the stability of the neurocontrolled state trajectories. We\nexemplify the proposed methods in the case of the two-dimensional dynamics of a\nquadcopter controlled to reach the origin and we study how different\narchitectures of the guidance and control network affect the stability of the\ntarget equilibrium point and the stability margins to time delay. Moreover, we\nshow how to study the robustness to initial conditions of a nominal trajectory,\nusing a Taylor representation of the neurocontrolled neighbouring trajectories.","url_abs":"http://arxiv.org/abs/1812.02532v3","url_pdf":"http://arxiv.org/pdf/1812.02532v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-the-stability-analysis-of-optimal-state","repo_url":"https://github.com/darioizzo/neurostability","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"imitation-learning","task_name":"Imitation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}