| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 102 | |
| Number of page(s) | 33 | |
| DOI | https://doi.org/10.1051/cocv/2025088 | |
| Published online | 07 January 2026 | |
Pattern-preserving optimal control problems with increasing time horizon
1
Dipartimento di Elettronica e Telecomunicazioni (DET), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universitá di Udine, via delle Scienze 206, 33100 Udine, Italy
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
12
June
2025
Accepted:
1
November
2025
Abstract
We establish a general framework that guarantees the preservation of optimal control patterns as the time horizon [0, T] increases and becomes unbounded. A concept of pattern-preserving family of optimal control problems is introduced and the goal is achieved by analyzing the Γ-convergence of the corresponding variational formulations as T → ∞. Special attention is given to scenarios involving state constraints. To illustrate the results, examples and applications are provided, with particular focus on switched systems and epidemic control.
Mathematics Subject Classification: 49J15 / 49J45 / 93C15
Key words: Optimal control / pattern-preserving sequence / infinite horizon / state constraints / Γ-convergence / coercivity / epidemic control / switched systems
© The authors. Published by EDP Sciences, SMAI 2026
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