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    Geometric control and disturbance decoupling for fractional systems

    89311.pdf (1.576Mb)
    Access Status
    Open access
    Authors
    Padula, Fabrizio
    Ntogramatzidis, Lorenzo
    Schmid, R.
    Loxton, Ryan
    Date
    2020
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Padula, F. and Ntogramatzidis, L. and Schmid, R. and Loxton, R. 2020. Geometric control and disturbance decoupling for fractional systems. SIAM Journal on Control and Optimization. 58 (3): pp. 1403-1428.
    Source Title
    SIAM Journal on Control and Optimization
    DOI
    10.1137/19M1261493
    ISSN
    0363-0129
    Faculty
    Faculty of Science and Engineering
    School
    School of Elec Eng, Comp and Math Sci (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/89487
    Collection
    • Curtin Research Publications
    Abstract

    We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance decoupling problem via static pseudostate feedback, with and without stability. Our main contribution is a set of necessary and sufficient conditions for the disturbance decoupling problem that are related to the input-output properties of the closed-loop system, and hence they are applicable not just to Caputo-type derivatives but, more broadly, to any type of fractional system. These results show that, while the conditions for guaranteeing the existence of a decoupling pseudostate feedback remain essentially unchanged, the underlying theoretical framework is substantially different, because the fractional derivative is a nonlocal operator and this property plays a major role in the characterization of the evolution of the pseudostate trajectory. In particular, we show that, unlike the integer case, the infinite-dimensional nature of fractional systems means that feedback control is insufficient to maintain the pseudostate trajectory on a controlled invariant subspace, unless the entire past history of the pseudostate has evolved on that subspace. However, feedforward control can achieve this task under certain necessary and sufficient geometric conditions.

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