Titelaufnahme

Titel
Polynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs
Verfasser/ VerfasserinKalise, Dante ; Kunisch, Karl
Erschienen in
SIAM Journal on Scientific Computing, 2018, Jg. 40, H. 2, S. A629-A652
ErschienenSIAM, 2018
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)optimal feedback control / Hamilton-Jacobi-Bellman equations / nonlinear dynamics / polynomial approximation / high-dimensional approximation
Projekt-/ReportnummerERC advanced Grant 668998 (OCLOC)
URNurn:nbn:at:at-ubg:3-5199 Persistent Identifier (URN)
DOI10.1137/17M1116635 
Zugriffsbeschränkung
 Das Werk ist frei verfügbar
Dateien
Polynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs [3.47 mb]
Links
Nachweis
Klassifikation
Zusammenfassung (Englisch)

A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are a pseudospectral collocation approximation of the PDE dynamics and an iterative method for the nonlinear HJB equation associated to the feedback synthesis. The latter is known as the successive Galerkin approximation. It can also be interpreted as Newton iteration for the HJB equation. At every step, the associated linear generalized HJB equation is approximated via a separable polynomial approximation ansatz. Stabilizing feedback controls are obtained from solutions to the HJB equations for systems of dimension up to fourteen.

Notiz
Statistik
Das PDF-Dokument wurde 3 mal heruntergeladen.