A radial basis collocation method for Hamilton-Jacobi-Bellman equations

C-S. Huang, Song Wang, C.S. Chen, Z-C. Li

    Research output: Contribution to journalArticle

    21 Citations (Scopus)

    Abstract

    In this paper we propose a semi-meshless discretization method for the approximation of viscosity solutions to a first order Hamilton-Jacobi-Bellman (HJB) equation governing a class of nonlinear optimal feedback control problems. In this method, the spatial discretization is based on a collocation scheme using the global radial basis functions (RBFs) and the time variable is discretized by a standard two-level time-stepping scheme with a splitting parameter theta. A stability analysis is performed, showing that even for the explicit scheme that theta=0, the method is stable in time. Since the time discretization is consistent, the method is also convergent in time. Numerical results, performed to verify the usefulness of the method, demonstrate that the method gives accurate approximations to both of the control and state variables. (c) 2006 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)2201-2207
    JournalAutomatica
    Volume42
    Issue number12
    DOIs
    Publication statusPublished - 2006

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    Cite this

    Huang, C-S. ; Wang, Song ; Chen, C.S. ; Li, Z-C. / A radial basis collocation method for Hamilton-Jacobi-Bellman equations. In: Automatica. 2006 ; Vol. 42, No. 12. pp. 2201-2207.
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    abstract = "In this paper we propose a semi-meshless discretization method for the approximation of viscosity solutions to a first order Hamilton-Jacobi-Bellman (HJB) equation governing a class of nonlinear optimal feedback control problems. In this method, the spatial discretization is based on a collocation scheme using the global radial basis functions (RBFs) and the time variable is discretized by a standard two-level time-stepping scheme with a splitting parameter theta. A stability analysis is performed, showing that even for the explicit scheme that theta=0, the method is stable in time. Since the time discretization is consistent, the method is also convergent in time. Numerical results, performed to verify the usefulness of the method, demonstrate that the method gives accurate approximations to both of the control and state variables. (c) 2006 Elsevier Ltd. All rights reserved.",
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    A radial basis collocation method for Hamilton-Jacobi-Bellman equations. / Huang, C-S.; Wang, Song; Chen, C.S.; Li, Z-C.

    In: Automatica, Vol. 42, No. 12, 2006, p. 2201-2207.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A radial basis collocation method for Hamilton-Jacobi-Bellman equations

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    AU - Wang, Song

    AU - Chen, C.S.

    AU - Li, Z-C.

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    AB - In this paper we propose a semi-meshless discretization method for the approximation of viscosity solutions to a first order Hamilton-Jacobi-Bellman (HJB) equation governing a class of nonlinear optimal feedback control problems. In this method, the spatial discretization is based on a collocation scheme using the global radial basis functions (RBFs) and the time variable is discretized by a standard two-level time-stepping scheme with a splitting parameter theta. A stability analysis is performed, showing that even for the explicit scheme that theta=0, the method is stable in time. Since the time discretization is consistent, the method is also convergent in time. Numerical results, performed to verify the usefulness of the method, demonstrate that the method gives accurate approximations to both of the control and state variables. (c) 2006 Elsevier Ltd. All rights reserved.

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