An adaptive multilevel radial basis function scheme for the HJB equation

G. Ferretti; R. Ferretti; O. Junge; A. Schreiber

doi:10.1016/j.ifacol.2017.08.331

An adaptive multilevel radial basis function scheme for the HJB equation

G. Ferretti, R. Ferretti, O. Junge, A. Schreiber

Associate Professorship of Numerics of Complex Systems

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The globally optimal solution of an optimal control problem can be characterized in terms of the value function. This function can be computed as the solution of the Hamilton-Jacobi-Bellman PDE or the equivalent Bellman equation. We propose an adaptive multilevel scheme based on radial basis functions for space discretizing these equations and demonstrate the efficiency of this approach by numerical experiments.

Original language	English
Pages (from-to)	1643-1648
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	50
Issue number	1
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.331
State	Published - Jul 2017

Keywords

Bellman equation
HJB equation
Shepard's method
adaptivity
multilevel scheme
optimal control
radial basis function
value function

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10.1016/j.ifacol.2017.08.331

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abstract = "The globally optimal solution of an optimal control problem can be characterized in terms of the value function. This function can be computed as the solution of the Hamilton-Jacobi-Bellman PDE or the equivalent Bellman equation. We propose an adaptive multilevel scheme based on radial basis functions for space discretizing these equations and demonstrate the efficiency of this approach by numerical experiments.",

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AU - Junge, O.

AU - Schreiber, A.

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KW - HJB equation

KW - Shepard's method

KW - adaptivity

KW - multilevel scheme

KW - optimal control

KW - radial basis function

KW - value function

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An adaptive multilevel radial basis function scheme for the HJB equation

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Keywords

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