Design of interval observers and controls for PDEs using finite-element approximations. (July 2018)

• Record Type: Journal Article
• Authors: Kharkovskaya, Tatiana; Efimov, Denis; Polyakov, Andrey; Richard, Jean-Pierre
• Is Part Of: Automatica. Volume 93(2018)
• Page Start: 302
• Page End: 310
• Publication Date: 2018-07
• Subjects: Interval observers -- PDE -- Finite-element approximation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.03.016
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.