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Publication Date:
March 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2006.173

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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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

Delfim F. M. Torres1

1Control Theory Group (cotg), Centre for Research in Optimization and Control, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal. E-mail: delfim@mat.ua.pt

Citation Information: Georgian Mathematical Journal. Volume 13, Issue 1, Pages 173–182, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2006.173, March 2010

Publication History:
Received:
2005-05-16
Published Online:
2010-03-10

Abstract

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.

Key words and phrases:: Multicriteria optimal control systems; Noether symmetry principle; optimization with vector-valued cost; necessary conditions for unimprovable-Pareto-optimality; isoperimetric constraints

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