Voir la notice de l'article provenant de la source Numdam
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of the Hamilton–Jacobi–Bellman equation. The terms of the approximations are described by multilinear forms, which can be obtained as solutions to generalized Lyapunov equations with recursively defined right-hand sides. They form the basis for defining a suboptimal feedback law. The approximation properties of this feedback law are investigated. An application to the optimal control of a Fokker–Planck equation is also provided.
Keywords: Value function, Hamilton–Jacobi–Bellman equation, Bilinear control systems, Riccati equation, Generalized Lyapunov equations, Fokker–Planck equation
Breiten, Tobias 1 ; Kunisch, Karl 1, 2 ; Pfeiffer, Laurent 1
@article{AIHPC_2019__36_5_1361_0,
author = {Breiten, Tobias and Kunisch, Karl and Pfeiffer, Laurent},
title = {Taylor expansions of the value function associated with a bilinear optimal control problem},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1361--1399},
publisher = {Elsevier},
volume = {36},
number = {5},
year = {2019},
doi = {10.1016/j.anihpc.2019.01.001},
mrnumber = {3985547},
zbl = {1420.49005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.01.001/}
}
TY - JOUR AU - Breiten, Tobias AU - Kunisch, Karl AU - Pfeiffer, Laurent TI - Taylor expansions of the value function associated with a bilinear optimal control problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2019 SP - 1361 EP - 1399 VL - 36 IS - 5 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.01.001/ DO - 10.1016/j.anihpc.2019.01.001 LA - en ID - AIHPC_2019__36_5_1361_0 ER -
%0 Journal Article %A Breiten, Tobias %A Kunisch, Karl %A Pfeiffer, Laurent %T Taylor expansions of the value function associated with a bilinear optimal control problem %J Annales de l'I.H.P. Analyse non linéaire %D 2019 %P 1361-1399 %V 36 %N 5 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.01.001/ %R 10.1016/j.anihpc.2019.01.001 %G en %F AIHPC_2019__36_5_1361_0
Breiten, Tobias; Kunisch, Karl; Pfeiffer, Laurent. Taylor expansions of the value function associated with a bilinear optimal control problem. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 5, pp. 1361-1399. doi: 10.1016/j.anihpc.2019.01.001
Cité par Sources :