A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory

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) n...

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Bibliographic Details
Published inGeorgian mathematical journal Vol. 13; no. 1; pp. 173 - 182
Main Author Torres, Delfim F. M.
Format Journal Article
LanguageEnglish
Published Walter de Gruyter GmbH & Co. KG 01.03.2006
De Gruyter
Subjects
isoperimetric constraints
Multicriteria optimal control systems
necessary conditions for unimprovable-Pareto-optimality
Noether symmetry principle
optimization with vector-valued cost
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Summary: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.
Bibliography:ArticleID:GMJ.13.1.173
istex:8E0BCE21AD5D10FBFF21F7BE7C54FB3D269BAAEB
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gmj.2006.173.pdf
ISSN:1072-947X
1072-9176
1572-9176
DOI:10.1515/GMJ.2006.173