Journal of Global Optimization
, Volume 27, Issue 2, pp 177192
First online:
Numerical Solution of HamiltonJacobiBellman Equations by an Upwind Finite Volume Method
 S. WangAffiliated withCentre for Applied Dynamics and Optimization, Department of Mathematics and Statistics, The University of Western Australia
 , L.S. JenningsAffiliated withCentre for Applied Dynamics and Optimization, Department of Mathematics and Statistics, The University of Western Australia
 , K.L. TeoAffiliated withDepartment of Applied Mathematics, Hong Kong Polytechnic University
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In this paper we present a finite volume method for solving HamiltonJacobiBellman(HJB) equations governing a class of optimal feedback control problems. This method is based on a finite volume discretization in state space coupled with an upwind finite difference technique, and on an implicit backward Euler finite differencing in time, which is absolutely stable. It is shown that the system matrix of the resulting discrete equation is an Mmatrix. To show the effectiveness of this approach, numerical experiments on test problems with up to three states and two control variables were performed. The numerical results show that the method yields accurate approximate solutions to both the control and the state variables.
 Title
 Numerical Solution of HamiltonJacobiBellman Equations by an Upwind Finite Volume Method
 Journal

Journal of Global Optimization
Volume 27, Issue 23 , pp 177192
 Cover Date
 200311
 DOI
 10.1023/A:1024980623095
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Optimal feedback control
 HamiltonJacobiBellman equation
 finite volume method
 Viscosity solution
 upwind finite difference
 Industry Sectors
 Authors

 S. Wang ^{(1)}
 L.S. Jennings ^{(1)}
 K.L. Teo ^{(2)}
 Author Affiliations

 1. Centre for Applied Dynamics and Optimization, Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
 2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong