Quasi-Invariant Optimal Control Problems
Abstract
Description
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate a more general version of Noether's theorem for optimal control problems, which incorporates the possibility to consider a family of transformations depending on several parameters and, what is more important, to deal with quasi-invariant and not necessarily invariant optimal control problems. We trust that this latter extension provides new possibilities and we illustrate it with several examples, not covered by the previous known optimal control versions of Noether's theorem.
Partially presented at the Invited Session "Control, Optimization and Computation", 10th Mediterranean Conference on Control and Automation (MED2002), Lisbon, July 9-12, 2002. Accepted for publication (21.Feb.03) in the journal Portugaliae Mathematica. See http://www.mat.ua.pt/delfim for other works
Partially presented at the Invited Session "Control, Optimization and Computation", 10th Mediterranean Conference on Control and Automation (MED2002), Lisbon, July 9-12, 2002. Accepted for publication (21.Feb.03) in the journal Portugaliae Mathematica. See http://www.mat.ua.pt/delfim for other works