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    The generalised discrete algebraic Riccati equation in linear-quadratic optimal control

    196118_196118.pdf (195.9Kb)
    Access Status
    Open access
    Authors
    Ferrante, A.
    Ntogramatzidis, Lorenzo
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Ferrante, Augusto and Ntogramatzidis, Lorenzo. 2013. The generalised discrete algebraic Riccati equation in linear-quadratic optimal control. Automatica. 49 (2): pp. 471-478.
    Source Title
    Automatica
    DOI
    10.1016/j.automatica.2012.11.006
    ISSN
    0005-1098
    Remarks

    NOTICE: this is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, Vol. 49, No. 2 (2013). DOI: 10.1016/j.automatica.2012.11.006

    URI
    http://hdl.handle.net/20.500.11937/40052
    Collection
    • Curtin Research Publications
    Abstract

    This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing the main results of this paper, several ancillary problems on the discrete Lyapunov equation and spectral factorisation are also addressed and solved.

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