Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction
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Publication:6322810
arXiv1907.12155MaRDI QIDQ6322810
Author name not available (Why is that?)
Publication date: 25 July 2019
Abstract: We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method.
Has companion code repository: https://bitbucket.org/alecoent/oslator
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