Georgian Mathematical Journal 13 (2006), No. 1, 173--182
Copyright Heldermann Verlag 2006
A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory
Delfim F. M. Torres
Control Theory Group, Centre for Research in Optimization and Control, Dept. of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
delfim@mat.ua.pt
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 for optimal control problems subject to isoperimetric constraints, and then using the unimprovable (Pareto) notion of optimality. It was A. Gugushvili who drew the author's attention to a result of this kind that was posed as an open mathematical question of a great interest in applications of control engineering.
Keywords: Multicriteria optimal control systems, Noether symmetry principle, optimization with vector-valued cost, necessary conditions for unimprovable Pareto optimality, isoperimetric constraints.
MSC: 49K15, 49N99, 93C10
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