Geodesic
Static PDEs for time-dependent control problems
Alexander Vladimirsky1
1Cornell University, Ithaca, United States
Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 281-300

Voir la notice de l'article provenant de la source EMS Press

DOI

We consider two different non-autonomous anisotropic time-optimal control problems. For the min-time-from-boundary problem, we show that the value function is recovered as a viscosity solution of a static Hamilton–Jacobi–Bellman partial differential equation H(∇u(x),u(x),x)=1. We demonstrate that the space-marching Ordered Upwind Methods (introduced in [29] for the autonomous control) can be extended to this non-autonomous case. We illustrate this approach with several numerical experiments. For the min-time-to-boundary problem, where no reduction to a static PDE is possible, we show how the space-marching methods can be efficiently used to approximate individual level sets of the time-dependent value function.
DOI : 10.4171/ifb/144
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Alexander Vladimirsky  1

1 Cornell University, Ithaca, United States 
Alexander Vladimirsky. Static PDEs for time-dependent control problems. Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 281-300. doi: 10.4171/ifb/144
@article{10_4171_ifb_144,
     author = {Alexander Vladimirsky},
     title = {Static {PDEs} for time-dependent control problems},
     journal = {Interfaces and free boundaries},
     pages = {281--300},
     year = {2006},
     volume = {8},
     number = {3},
     doi = {10.4171/ifb/144},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/144/}
}
TY  - JOUR
AU  - Alexander Vladimirsky
TI  - Static PDEs for time-dependent control problems
JO  - Interfaces and free boundaries
PY  - 2006
SP  - 281
EP  - 300
VL  - 8
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/144/
DO  - 10.4171/ifb/144
ID  - 10_4171_ifb_144
ER  - 
%0 Journal Article
%A Alexander Vladimirsky
%T Static PDEs for time-dependent control problems
%J Interfaces and free boundaries
%D 2006
%P 281-300
%V 8
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/144/
%R 10.4171/ifb/144
%F 10_4171_ifb_144

Cité par Sources :