We consider the prototypical example of the 2 x 2 liquid chromatography system and characterize the set of initial data leading to a given attainable profile at t = T. For profiles that are not attainable at time T, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the L-2-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz-Kranzer system.
Inverse design and boundary controllability for the chromatography system
De Nitti N;
2024-01-01
Abstract
We consider the prototypical example of the 2 x 2 liquid chromatography system and characterize the set of initial data leading to a given attainable profile at t = T. For profiles that are not attainable at time T, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the L-2-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz-Kranzer system.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
