Optimal sampled-data control, and generalizations on time scales

Loïc  Bourdin; Emmanuel Trélat

doi:10.3934/mcrf.2016.6.53

Article Contents

2016, Volume 6, Issue 1: 53-94. Doi: 10.3934/mcrf.2016.6.53

This issue Previous Article Quantification of the unique continuation property for the nonstationary Stokes problem Next Article Optimal control for a phase field system with a possibly singular potential

Optimal sampled-data control, and generalizations on time scales

Loïc Bourdin^1, and
Emmanuel Trélat^2,

1.
Université de Limoges, Institut de recherche XLIM, Département de Mathématiques et d'Informatique, CNRS UMR 7252, Limoges
2.
Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Institut Universitaire de France, F-75005, Paris

Received: December 31, 2014

Revised: September 30, 2015

Published: February 2016

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Abstract

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for which the state variable evolves on a given time scale (arbitrary non-empty closed subset of $\mathbb{R}$), and the control variable evolves on a smaller time scale. Sampled-data systems are then a particular case. Our proof is based on the construction of appropriate needle-like variations and on the Ekeland variational principle.

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Mathematics Subject Classification: 49J15, 93C57, 34N99, 39A12.

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