Numerical solution of Hamilton-Jacobi-Bellman equations by an exponentially fitted finite volume method

Steven Richardson, Song Wang

    Research output: Contribution to journalArticle

    16 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)121-140
    JournalOptimization
    Volume55
    Issue number1/52
    DOIs
    Publication statusPublished - 2006

    Fingerprint

    Hamilton-Jacobi-Bellman Equation
    Finite volume method
    Finite Volume Method
    Numerical Solution
    Feedback control
    Optimal Feedback Control
    Numerical methods
    Unconditionally Stable
    M-matrix
    Discrete Equations
    Time Discretization
    Finite Volume
    Finite Difference Scheme
    Test Problems
    Euler
    Control Problem
    State Space
    Approximate Solution
    Discretization
    Numerical Methods

    Cite this

    Richardson, Steven ; Wang, Song. / Numerical solution of Hamilton-Jacobi-Bellman equations by an exponentially fitted finite volume method. In: Optimization. 2006 ; Vol. 55, No. 1/52. pp. 121-140.
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    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.",
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    Numerical solution of Hamilton-Jacobi-Bellman equations by an exponentially fitted finite volume method. / Richardson, Steven; Wang, Song.

    In: Optimization, Vol. 55, No. 1/52, 2006, p. 121-140.

    Research output: Contribution to journalArticle

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    AB - 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.

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