Design of interval observers and controls for PDEs using finite-element approximations

Synthesis of interval state estimators is investigated for the systems described by a class of parabolic Partial Differential Equations (PDEs). First, a finite-element approximation of a PDE is constructed and the design of an interval observer for the derived ordinary differential equation is given...

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Veröffentlicht in:Automatica (Oxford) 2018-07, Vol.93, p.302-310
Hauptverfasser: Kharkovskaya, Tatiana, Efimov, Denis, Polyakov, Andrey, Richard, Jean-Pierre
Format: Artikel
Sprache:eng
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Zusammenfassung:Synthesis of interval state estimators is investigated for the systems described by a class of parabolic Partial Differential Equations (PDEs). First, a finite-element approximation of a PDE is constructed and the design of an interval observer for the derived ordinary differential equation is given. Second, the interval inclusion of the state function of the PDE is calculated using the error estimates of the finite-element approximation. Finally, the obtained interval estimates are used to design a dynamic output stabilizing control. The results are illustrated by numerical experiments with an academic example and the Black–Scholes model of financial market.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2018.03.016