  We obtain a version of Noether's invariance theorem for optimal control
problems with a finite number of cost functionals. The result is obtained by
formulating E. Noether's result to optimal control problems subject to
isoperimetric constraints, and then using the unimprovable (Pareto) notion of
optimality. A result of this kind was posed to the author, as a mathematical
open question, of great interest in applications of control engineering, by A.
Gugushvili.
