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 to optimal control problems subject to isoperimetric constraints, and then using the unimprovable (Pareto) no...

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Bibliographic Details
Published inarXiv.org
Main Author Torres, Delfim F M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.11.2004
Subjects
Conservation laws
Control theory
Optimal control
Optimization
Theorems
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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 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.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422
DOI:10.48550/arxiv.0411173