Convergence of an Upwind Finite-Difference Scheme for Hamilton-Jacobi-Bellman Equation in Optimal Control

This technical note considers convergence of an upwind finite-difference numerical scheme for the Hamilton-Jacobi-Bellman equation arising in optimal control. This effective scheme has been well-adapted and successfully applied to many examples. Nevertheless, its convergence has remained open until...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on automatic control Vol. 60; no. 11; pp. 3012 - 3017
Main Authors Sun, Bing, Guo, Bao-Zhu
Format Journal Article
LanguageEnglish
Published New York IEEE 01.11.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Approximation methods
Automatic control
Convergence
Equations
Feedback control
Finite difference method
finite-difference
Hamilton-Jacobi-Bellman equation
Mathematical analysis
Mathematical model
Mathematical models
numerical approximation
Optimal control
Viscosity
Hamilton–Jacobi–Bellman equation
optimal control
finite-difference
numerical approximation
Convergence
Online AccessGet full text

Cover

More Information
Summary:This technical note considers convergence of an upwind finite-difference numerical scheme for the Hamilton-Jacobi-Bellman equation arising in optimal control. This effective scheme has been well-adapted and successfully applied to many examples. Nevertheless, its convergence has remained open until now. In this note, we show that the solution from this finite-difference scheme converges to the value function of the associated optimal control problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2406976