OPTIMAL CONTROL PROBLEMS DRIVEN BY TIME-FRACTIONAL DIFFUSION EQUATIONS ON METRIC GRAPHS: OPTIMALITY SYSTEM AND FINITE DIFFERENCE APPROXIMATION
Mehandiratta V, Mehra M, Leugering G (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 59
Pages Range: 4216-4242
Journal Issue: 6
DOI: 10.1137/20M1340332
Abstract
We study optimal control problems for time-fractional diffusion equations on metric graphs, where the fractional derivative is considered in the Caputo sense. Using eigenfunction expansions for the spatial part, we first prove the well-posedness of the system. We then prove the existence of a unique solution to the optimal control problem, where we admit both boundary and distributed controls. We develop an adjoint calculus for the right Caputo derivative and derive the corresponding first order optimality system. We also propose a finite difference approximation to find the numerical solution of the optimality system on the graph. In the proposed method, the so-called Ll method is used for the discrete approximation of the Caputo derivative, while the space derivative is approximated using a standard central difference scheme, which results in converting the optimality system into a system of algebraic equations. Finally, an example is provided to demonstrate the performance of the numerical method.
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APA:
Mehandiratta, V., Mehra, M., & Leugering, G. (2021). OPTIMAL CONTROL PROBLEMS DRIVEN BY TIME-FRACTIONAL DIFFUSION EQUATIONS ON METRIC GRAPHS: OPTIMALITY SYSTEM AND FINITE DIFFERENCE APPROXIMATION. SIAM Journal on Control and Optimization, 59(6), 4216-4242. https://doi.org/10.1137/20M1340332
MLA:
Mehandiratta, Vaibhav, Mani Mehra, and Günter Leugering. "OPTIMAL CONTROL PROBLEMS DRIVEN BY TIME-FRACTIONAL DIFFUSION EQUATIONS ON METRIC GRAPHS: OPTIMALITY SYSTEM AND FINITE DIFFERENCE APPROXIMATION." SIAM Journal on Control and Optimization 59.6 (2021): 4216-4242.
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