Naslov
Greedy control

Autori
Lazar, Martin ; Zuazua, Enrique

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo

Izvornik
7th European Congress of Mathematics, Berlin, 18-22. 07. 2016. / - , 2016, 1-1

Skup
7th European Congress of Mathematics

Mjesto i datum
Berlin, Njemačka, 18.07.2016. - 22.07.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

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

Sažetak
In this talk we discuss a new approach to the problem of controllability for parameter dependent systems. It is based on adaptation of (weak) greedy algorithms, originally developed for constructing an approximative solutions to parametric PDEs. The idea is to identify the most distinguished parameter values describing the whole range of admissible controls. The algorithm consists of the (possible expensive) offline part devoted to the selection of parameter representatives and the online one enabling a fast computation of an approximative control for a given value of the parameter within a prescribed accuracy. Our results lead to optimal approximation rates expressed in terms of Kolmogorov widths. These results are applied to 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