Quasi-Invariant Optimal Control Problems

Abstract

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

References in corpus (1)

• A Remarkable Property of the Dynamic Optimization Extremals

Cited by in corpus (15)

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• Symbolic Computation of Variational Symmetries in Optimal Control
• Noether's Theorem for Control Problems on Time Scales
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• A Non-Newtonian Noether's Symmetry Theorem
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• Absolute Extrema of Invariant Optimal Control Problems
• A formulation of Noether's theorem for fuzzy problems of the calculus of variations