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

Georgian Mathematical Journal, Vol.13 (2006), No1, pp. 173--182 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 isoper...

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Bibliographic Details
Main Author Torres, Delfim F. M
Format Journal Article
LanguageEnglish
Published 08.11.2004
Subjects
Mathematics - Mathematical Physics
Mathematics - Optimization and Control
Physics - Mathematical Physics
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Summary:Georgian Mathematical Journal, Vol.13 (2006), No1, pp. 173--182 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.
DOI:10.48550/arxiv.math/0411173