2003/01/11 by Delfim F. M. Torres
Mathematics · #math.OC #msc:49K15 #msc:49S05
published as Appl. Math. E-Notes 3 (2003), 49--57 (electronic). · Partially presented at the 5th Portuguese Conference on Automatic Control (Controlo 2002), Aveiro, Portugal, September 5-7, 2002. Accepted for publication in Applied Mathematics E-Notes, Volume 3. See http://www.mat.ua.pt/delfim for other works
arxiv created 2003/01/11 · arxiv updated 2009/11/30
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a semi-invariance notion, and the transformation group may also depend on the control variables, the result is new even in the classical context of the calculus of variations.