An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation
type: Item
instance of: scholarly article
title: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation
zbMATH Open document ID: 0880.65045
author: Lars Grüne
published in: Numerische Mathematik
publication date: 1997-06-30T00:00:00Z
full work available at URL: gruene num math 1997.pdf
review text: An adaptive grid scheme for the solution of the discrete first order Hamilton-Jacobi-Bellmann equation \[ \sup_{u\in U}\{v_h(x)-\beta v_h(\Phi_h(x,u))- hg(x,u)\}=0 \] on \(\Omega\subset \mathbb R^n\) with \(0<\beta<1\) is developed, where \(\Phi_h\) is the right hand side of a discrete time control system and \(g\) is the cost function. Error estimates are proved and an adapting iteration for the discretization of the state space is developed.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 1027737
zbMATH Keywords: finite difference method
zbMATH Keywords: error estimates
zbMATH Keywords: adaptive grid scheme
zbMATH Keywords: Hamilton-Jacobi-Bellmann equation
zbMATH Keywords: discrete time control system
reviewed by: Hans Benker
MaRDI profile type: Publication
OpenAlex ID: W2058212189
DOI: 10.1007/S002110050241
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description: scientific article; zbMATH DE number 1027737