| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 61 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/cocv/2019038 | |
| Published online | 18 September 2020 | |
Sparse and switching infinite horizon optimal controls with mixed-norm penalizations
1
School of Mathematical Sciences, University of Nottingham, University Park,
Nottingham
NG7 2QL, UK.
2
Institute for Mathematics and Scientific Computing, University of Graz,
Heinrichstraße 36,
8010 Graz, Austria.
3
Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences,
A-4040 Linz, Austria.
4
School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Sciences, Wuhan University,
Wuhan 430072,
Hubei, PR China.
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
31
August
2018
Accepted:
5
June
2019
Abstract
A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.
Mathematics Subject Classification: 93D15 / 93B52 / 93C05 / 93C20
Key words: Optimal control / infinite horizon control / sparse controls / switching controls / optimality conditions / dynamic programming
Research supported by the Imperial College London Research Fellowship program.
Research in part supported by the ERC advanced grant 668998 (OCLOC) under the EU's H2020 research program.
Research in part supported by NSFC 11801422.
© EDP Sciences, SMAI 2020
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