Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

Adrien Le Coënt; Laurent Fribourg

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arXiv · 1907.12155

Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

Adrien Le Coënt·Laurent Fribourg

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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.

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BibTeX RIS

Adrien Le Coënt, Laurent Fribourg. 2019-07-25. Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction. https://arxiv.org/abs/1907.12155

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