2017/04/01 by Simao P. S. Santos, Simão P. S. Santos, Natália Martins +2 · 20 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Computer science #Geometry #Lagrangian #Mathematical analysis #Mathematical optimization #Mathematics #Noether's theorem #Nonlinear Partial Differential Equations #Optimal control #Order (exchange) #Perspective (graphical) #Rewriting #Stability and Controllability of Differential Equations #Type (biology) #Variational principle #math-ph #math.MP #math.OC #msc:34H05 #msc:49K05 #msc:49K15 #msc:49S05
paper · pdf · doi:10.3934/dcdss.2018006
published in Discrete and Continuous Dynamical Systems - S 11(1), 91-102 (American Institute of Mathematical Sciences) · This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S), ISSN 1937-1632 (print), ISSN 1937-1179 (online), available at [https://www.aimsciences.org/journals/home.jsp?journalID=15]. Paper Submitted 01-Oct-2016; Revised 01 and 21 March-2017; Accepted 31-March-2017
arxiv created 2017/04/01 · openalex publication_date 2017/10/10 · arxiv updated 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful in the search of extremals. The proof is based on the idea of rewriting the higher-order delayed generalized variational problem as a first-order optimal control problem without time delays.