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