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    Linear-quadratic control for stochastic equations in a Hilbert space with a fractional Brownian motion

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    Issue Date
    2012-01-01
    Author
    Duncan, Tyrone E.
    Maslowski, Bozenna J.
    Pasik-Duncan, Bozenna
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    Abstract
    A linear-quadratic control problem with a finite time horizon for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well-known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system response to the future noise. The covariance of the noise as well as the control operator in the system equation can in general be unbounded, so the results can also be applied where the noise or the control are on the boundary of the domain or at discrete points in the domain. Some examples of controlled stochastic partial differential equations are given.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/110831416.
    URI
    http://hdl.handle.net/1808/16690
    DOI
    https://doi.org/10.1137/110831416
    Collections
    • Aerospace Engineering Scholarly Works [49]
    • Mathematics Scholarly Works [282]
    Citation
    Duncan, Tyrone E. "Linear-quadratic control for stochastic equations in a Hilbert space with a fractional Brownian motion." SIAM J. Control Optim. (2012) 50 , 1. 507-531. http://www.dx.doi.org/10.1137/110831416.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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