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

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 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.

To appear (paper ID: 131) in the Conference Proceedings of ICMSAO'05 -- First International Conference on Modeling, Simulation and Applied Optimization, February 1-3 2005, American University of Sharjah, United Arab Emirates

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