American Institute of Mathematical Sciences

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January  2010, 6(1): 161-175. doi: 10.3934/jimo.2010.6.161

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, Australia
2. 

School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009

Received  June 2008 Revised  September 2009 Published  November 2009

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.
Keywords: Viscosity solutions, Hamilton-Jacobi-Bellman equation, Viscosity approximation, Domain of dependence., Optimal feedback Control.
Mathematics Subject Classification: Primary: 49N35; 49L25; Secondary: 35L6.
Citation: Steven Richardson, Song Wang. The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains. Journal of Industrial & Management Optimization, 2010, 6 (1) : 161-175. doi: 10.3934/jimo.2010.6.161
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