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.

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