Quadratures of Pontryagin Extremals for Optimal Control Problems

Details Quadratures of Pontryagin Extremals for Optimal Control Problems Quadratures of Pontryagin Extremals for Optimal Control Problems

2005-11-14

arxiv.org/abs/math/0511355v1

Control Cybernet. 35 (2006), no. 4, 947--963.

Mathematics

Optimization and Control

Presented at the 4th Junior European Meeting on "Control and Optimization", Bialystok Technical University, Bialystok, Poland,

Scientific paper

We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values on open sets is obtained. We illustrate our approach on some problems taken from the literature. An alternative proof of the integrability of the sub-Riemannian nilpotent Lie group of type (2,3,5) is also given.

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