doi:10.3934/dcdss.2023080engGhnatios, Chadydi Lorenzo, DanieleChampaney, VíctorCueto, ElíasChinesta, FranciscoOptimal velocity planning based on the solution of the Euler-Lagrange equations with a neural network based velocity regressionART-2023-133790Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations.2023http://zaguan.unizar.es/record/12660610.3934/dcdss.2023080http://zaguan.unizar.es/record/126606oai:zaguan.unizar.es:126606info:eu-repo/grantAgreement/ES/DGA-FSE/T24-20Rinfo:eu-repo/grantAgreement/EC/H2020/956401/EU/Cross-scale concurrent material-structure design using functionally-graded 3D-printed matematerials/XS-MetaThis project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 956401-XS-Metainfo:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-113463RB-C31/AEI/10.13039/501100011033info:eu-repo/grantAgreement/ES/UZ/UZ2019-0060Discrete and continuous dynamical systems. Series S 17, 7 (2023), 2323-2333All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess