Naslov
Greedy controllability of finite dimensional linear systems

Autori
Lazar, Martin ; Zuazua, Enrique

Izvornik
Automatica (0005-1098) 74 (2016); 327-340

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
parametrised ODEs and PDEs ; greedy control ; weak-greedy ; heat equation ; wave equation ; finite-differences

Sažetak
We analyse the problem of controllability for parameter dependent linear finite-dimensional systems. The goal is to identify the most distinguished realisations of those parameters so to better describe or approximate the whole range of controls. We adapt recent results on greedy and weak greedy algorithms for parameter dependent PDEs or, more generally, abstract equations in Banach spaces. Our results lead to optimal approximation procedures that, in particular, perform better than simply sampling the parameter-space to compute the controls for each of the parameter values. We apply these results for the approximate control of finite-difference approximations of the heat and the wave equation. The numerical experiments confirm the efficiency of the methods and show that the number of weak-greedy samplings that are required is particularly low when dealing with heat-like equations, because of the intrinsic dissipativity that the model introduces for high frequencies.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA