The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains
Steven Richardson - School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup 6027, 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.
Received: June 2008; Revised: September 2009; Available Online: November 2009.
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