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

Adrien Le Coënt (1) , Laurent Fribourg (2, 3, 4, 5)

1 Department of Computer Science [Aalborg]
2 LSV - Laboratoire Spécification et Vérification [Cachan]
3 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
4 CNRS - Centre National de la Recherche Scientifique
5 Université Paris-Saclay

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 control discretized systems of reaction-diffusion of larger dimension .

Domains: Systems and Control [cs.SY]

Adrien Le Coënt, Laurent Fribourg. Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction. 2019. ⟨hal-02193769v1⟩