The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains

Steven Richardson; Song Wang

doi:10.3934/jimo.2010.6.161

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2010, Volume 6, Issue 1: 161-175. Doi: 10.3934/jimo.2010.6.161

This issue Previous Article A derivative-free method for solving large-scale nonlinear systems of equations Next Article Global optimization algorithm for solving bilevel programming problems with quadratic lower levels

The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains

Steven Richardson^1, and
Song Wang^2,

1.
School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup 6027
2.
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009

Received: May 31, 2008

Revised: August 31, 2009

Published: December 2009

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Abstract

A number of numerical methods for solving optimal feedback control problems are based on the viscosity approximation to the Hamilton-Jacobi-Bellman (HJB) equation, with artificial boundary conditions defined on an extended domain. An upper bound for this extended domain is established, ensuring that the approximate solution converges to the viscosity solution of the HJB equation on some pre-defined domain of interest.

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Mathematics Subject Classification: Primary: 49N35; 49L25; Secondary: 35L60.

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