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Pré-Publication, Document De Travail Année : 2019

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

Résumé

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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Dates et versions

hal-02193769 , version 1 (24-07-2019)
hal-02193769 , version 2 (26-09-2019)
hal-02193769 , version 3 (09-12-2019)

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Adrien Le Coënt, Laurent Fribourg. Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction. 2019. ⟨hal-02193769v3⟩
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