Journal of Industrial and Management Optimization (JIMO)

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

Pages: 161 - 175, Volume 6, Issue 1, February 2010      doi:10.3934/jimo.2010.6.161

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Steven Richardson - School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup 6027, Australia (email)
Song Wang - School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia (email)

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.

Keywords:  Hamilton-Jacobi-Bellman equation, Optimal feedback Control, Viscosity approximation, Viscosity solutions, Domain of dependence.
Mathematics Subject Classification:  Primary: 49N35; 49L25; Secondary: 35L60.

Received: June 2008;      Revised: September 2009;      Available Online: November 2009.