| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 51 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/cocv/2021046 | |
| Published online | 04 June 2021 | |
Pontryagin maximum principle for state constrained optimal sampled-data control problems on time scales
1
Univ Brest, UMR CNRS 6205, Laboratoire de Mathématiques de Bretagne Atlantique,
29200
Brest, France.
2
Université de Limoges, UMR CNRS 7252, Institut de recherche XLIM,
87060, France.
* Corresponding author: piernicola.bettiol@univ-brest.fr
Received:
14
March
2020
Accepted:
22
April
2021
In this paper we consider optimal sampled-data control problems on time scales with inequality state constraints. A Pontryagin maximum principle is established, extending to the state constrained case existing results in the time scale literature. The proof is based on the Ekeland variational principle and on the concept of implicit spike variations adapted to the time scale setting. The main result is then applied to continuous-time min-max optimal sampled-data control problems, and a maximal velocity minimization problem for the harmonic oscillator with sampled-data control is numerically solved for illustration.
Mathematics Subject Classification: 26E70 / 34H05 / 34K35 / 34N05 / 39A12 / 49J15 / 49J50 / 93C10 / 93C15 / 93C57
Key words: Optimal control / Pontryagin maximum principle / sampled-data control / time scales, state constraints / Ekeland variational principle / implicit spike variations / min-max optimal control problems
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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