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

Mehandiratta V, Mehra M, Leugering G (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Control and Cybernetics Polish Academy of Sciences

Book Volume: 51

Pages Range: 191-226

Journal Issue: 2

DOI: 10.2478/candc-2022-0014

Abstract

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.

Authors with CRIS profile

Günter Leugering Naturwissenschaftliche Fakultät

Involved external institutions

Indian Institute of Technology (IIT), Delhi IN India (IN)

How to cite

APA:

Mehandiratta, V., Mehra, M., & Leugering, G. (2022). Distributed optimal control problems driven by space-time fractional parabolic equations. Control and Cybernetics, 51(2), 191-226. https://dx.doi.org/10.2478/candc-2022-0014

MLA:

Mehandiratta, Vaibhav, Mani Mehra, and Günter Leugering. "Distributed optimal control problems driven by space-time fractional parabolic equations." Control and Cybernetics 51.2 (2022): 191-226.

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