Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020, Pages 550 - 580

Study on geometric structures on Lie algebroids with optimal control applications

Authors
Esmaeil Peyghan
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran, e-peyghan@araku.ac.ir, epeyghan@gmail.com
Liviu Popescu*
Department of Statistics and Economic Informatics, Faculty of Economics and Business Administration, University of Craiova, 13 Al. I. Cuza st., 200585 Craiova, Romania, liviupopescu@central.ucv.ro, liviunew@yahoo.com
*Corresponding author.
Corresponding Author
Liviu Popescu
Received 30 July 2019, Accepted 5 December 2019, Available Online 4 September 2020.
DOI
https://doi.org/10.1080/14029251.2020.1819604How to use a DOI?
Keywords
Berwald and Yano-derivatives, Covariant derivative, Douglas tensor, Lie algebroid, Optimal control
Abstract

We construct ρ£-covariant derivatives in π*π as the generalization of covariant derivative in π*π to £πE. Moreover, we introduce Berwald and Yano derivatives as two important classes of ρ£-covariant derivatives in π*π and we study properties of them. Finally, we solve an optimal control problem using some geometric structures and Pontryagin Maximum Principle on Lie algebroids.

Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 4
Pages
550 - 580
Publication Date
2020/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1819604How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Esmaeil Peyghan
AU  - Liviu Popescu
PY  - 2020
DA  - 2020/09
TI  - Study on geometric structures on Lie algebroids with optimal control applications
JO  - Journal of Nonlinear Mathematical Physics
SP  - 550
EP  - 580
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819604
DO  - https://doi.org/10.1080/14029251.2020.1819604
ID  - Peyghan2020
ER  -