Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction
Optimization and Control
2019-12-12 v3 Systems and Control
Systems and Control
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.
Cite
@article{arxiv.1907.12155,
title = {Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction},
author = {Adrien Le Coënt and Laurent Fribourg},
journal= {arXiv preprint arXiv:1907.12155},
year = {2019}
}