| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 15 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2021014 | |
| Published online | 22 March 2021 | |
First and second order optimality conditions for the control of Fokker-Planck equations*
1
Escola de Matemática Aplicada, Fundação Getúlio Vargas,
Praia de Botafogo 190,
Rio de Janeiro
22250-900, Brazil.
2
Institut für Mathematik, Technische Universität Berlin,
Straße des 17. Juni 136,
10623
Berlin, Germany.
** Corresponding author: soledad.aronna@fgv.br
Received:
10
February
2020
Accepted:
2
February
2021
In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0
The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.
Mathematics Subject Classification: 49J20 / 49K20 / 49K27 / 35Q84
Key words: optimal control / Fokker-Planck equation / existence of optimal control / first order optimality conditions / second order optimality conditions
© EDP Sciences, SMAI 2021
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