Numerical solution of Hamilton-Jacobi-Bellman equations by an exponentially fitted finite volume method
Document Type
Journal Article
Publisher
Taylor and Francis
Faculty
Faculty of Computing, Health and Science
School
School of Engineering
RAS ID
8375
Abstract
In this article, we present a numerical method for solving Hamilton–Jacobi–Bellman (HJB) equations governing a class of optimal feedback control problems. This method is based on a finite volume discretisation in state space coupled with an exponentially fitted difference technique. The time discretisation of the method is the backward Euler finite difference scheme, which is unconditionally stable. It is shown that the system matrix of the resulting discrete equations is an M-matrix. To demonstrate the effectiveness of this approach, numerical experiments on test problems with up to three states and three control variables were performed. The numerical results show that the method yields accurate approximate solutions to both the control and state variables.
DOI
10.1080/02331930500530237
Comments
Richardson, S., & Wang, S. (2006). Numerical solution of Hamilton–Jacobi–Bellman equations by an exponentially fitted finite volume method. Optimization, 55(1-2), 121-140.