Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29370
Title: On application of an alternating direction method to Hamilton-Jacobin-Bellman equations
Authors: Huang, CS
Wang, S
Teo, KL
Keywords: Alternating direction method
Characteristic method
Finite difference method
Hamilton-Jacobi-Bellman equation
Optimal feedback control
Viscosity solution
Issue Date: 2004
Publisher: North-Holland
Source: Journal of computational and applied mathematics, 2004, v. 166, no. 1, p. 153-166 How to cite?
Journal: Journal of computational and applied mathematics 
Abstract: This paper presents a numerical method for the approximation of viscosity solutions to a Hamilton-Jacobi-Bellman (HJB) equation governing a class of optimal feedback control problems. The first-order HJB equation is first perturbed by adding a diffusion term with a singular perturbation parameter. The time and spatial variables in the resulting equation are then discretized respectively by an implicit modified method of characteristics and the alternating direction (AD) scheme. We show that the AD procedure's perturbation error is virtually negligible due to the small perturbation parameter. And the efficient AD scheme can be applied to our HJB equation without generating splitting error. Numerical results, performed to verify the usefulness of the method, show that the method gives accurate approximate solutions to both of the control and the state variables.
Description: Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Perth, Australia, 8-12 July 2002
URI: http://hdl.handle.net/10397/29370
ISSN: 0377-0427
EISSN: 1879-1778
DOI: 10.1016/j.cam.2003.09.031
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