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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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
08.11.2004
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| Online Access | Get full text |
| DOI | 10.48550/arxiv.math/0411173 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Torres, Delfim F. M |
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| BackLink | https://doi.org/10.1515/GMJ.2006.173$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.math/0411173$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Mathematics - Mathematical Physics Mathematics - Optimization and Control Physics - Mathematical Physics |
| Title | A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory |
| URI | https://arxiv.org/abs/math/0411173 |
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