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    The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control

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    Authors
    Ferrante, A.
    Ntogramatzidis, Lorenzo
    Date
    2014
    Type
    Journal Article
    
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    Citation
    Ferrante, Augusto and Ntogramatzidis, Lorenzo. 2014. The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control. Automatica. 50 (4): pp. 1176-1180.
    Source Title
    Automatica
    DOI
    10.1016/j.automatica.2014.02.014
    ISSN
    0005-1098
    URI
    http://hdl.handle.net/20.500.11937/6074
    Collection
    • Curtin Research Publications
    Abstract

    The purpose of this paper is to investigate the role that the so-called constrained generalized Riccati equation plays within the context of continuous-time singular linear–quadratic (LQ) optimal control. This equation has been defined following the analogy with the discrete-time setting. However, while in the discrete-time case the connections between this equation and the linear–quadratic optimal control problem have been thoroughly investigated, to date very little is known on these connections in the continuous-time setting. This note addresses this point. We show, in particular, that when the continuous-time constrained generalized Riccati equation admits a solution, the corresponding linear–quadratic problem admits an impulse-free optimal control. We also address the corresponding infinite-horizon LQ problem for which we establish a similar result under the additional constraint that there exists a control input for which the cost index is finite.

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