- Tytuł:
- Distributed optimal control problems driven by space-time fractional parabolic equations
- Autorzy:
-
Mehandiratta, Vaibhav
Mehra, Mani
Leugering, Günter - Powiązania:
- https://bibliotekanauki.pl/articles/2183495.pdf
- Data publikacji:
- 2022
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
space-time fractional parabolic equations
Caputo fractional derivative
distributed control
L1 method
Grünwald-Letnikov formula - Opis:
- We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.
- Źródło:
-
Control and Cybernetics; 2022, 51, 2; 191--226
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł