A splitting algorithm for Hamilton-Jacobi-Bellman equations
type: Item
instance of: scholarly article
title: A splitting algorithm for Hamilton-Jacobi-Bellman equations
zbMATH Open document ID: 0812.65050
DOI: 10.1016/0168-9274(94)00017-4
author: Piero Lanucara
author: Alessandra Seghini
author: M. Falcone
published in: Applied Numerical Mathematics
publication date: 1994-12-01T00:00:00Z
review text: The dynamic programming approach to the solution of deterministic optimal control problems gives the characterization of the value function in terms of a partial differential equation of the first order, the Hamilton-Jacobi-Bellman equation. This approach permits to compute controls in feedback form and, as a consequence, approximate optimal trajectories. The goal of this paper is to split up a problem given over a domain \(\Omega\) into a sequence of problems set in subdomains of manageable size \(\Omega_ r\), \(r= 1,\dots, d\). Roughly speaking, instead of one problem in dimension \(N\) the solutions of \(d\) problems in dimensions \(N_ r\), \(r= 1,\dots, d\) with \(N= N_ 1+\cdots+ N_ d\) are computed. In the last section results of some numerical experiments in \(\mathbb{R}^ 2\) are discussed.
reviewed by: Yves Cherruault
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49L99
zbMATH DE Number: 699069
zbMATH Keywords: viscosity solutions
zbMATH Keywords: domain decomposition
zbMATH Keywords: dynamic programming
zbMATH Keywords: deterministic optimal control problems
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: feedback
zbMATH Keywords: optimal trajectories
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)00017-4
OpenAlex ID: W2070376330
cites work: Q3490529
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description: scientific article; zbMATH DE number 699069