Distributed optimal control problems driven by space-time fractional parabolic equations

• Autorzy: Mehandiratta Vaibhav , Mehra Mani , Leugering Günter

Identyfikatory

DOI

10.2478/candc-2022-0014

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

space-time fractional parabolic equations; Caputo fractional derivative; distributed control; L1 method; Grünwald-Letnikov formula

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2022
• Tom: Vol. 51, No. 2
• Strony: 191--226
• Opis fizyczny: Bibliogr. 47 poz., rys., tab.

Twórcy

autor

Mehandiratta Vaibhav

• Department of Mathematics, Indian Institute of Technology, Delhi, India

autor

Mehra Mani

• Department of Mathematics, Indian Institute of Technology, Delhi, India

autor

Leugering Günter

• Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Senior Fellow of Applied Mathematics, Cauerstrasse 11, 91058 Erlangen, Germany

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