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A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

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  • Ivan Francisco Yupanqui Tello

    (Systems, Estimation, Control, and Optimization (SECO), University of Mons, 7000 Mons, Belgium
    Postgraduate Program in Engineering of Automation and Systems, Federal University of Santa Catarina, Florianopolis 88040-900, SC, Brazil
    These authors contributed equally to this work.)

  • Alain Vande Wouwer

    (Systems, Estimation, Control, and Optimization (SECO), University of Mons, 7000 Mons, Belgium
    These authors contributed equally to this work.)

  • Daniel Coutinho

    (Postgraduate Program in Engineering of Automation and Systems, Federal University of Santa Catarina, Florianopolis 88040-900, SC, Brazil
    These authors contributed equally to this work.)

Abstract

While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches.

Suggested Citation

  • Ivan Francisco Yupanqui Tello & Alain Vande Wouwer & Daniel Coutinho, 2021. "A Concise Review of State Estimation Techniques for Partial Differential Equation Systems," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3180-:d:698872
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    References listed on IDEAS

    as
    1. A. Vande Wouwer & C. Renotte & I. Queinnec & Ph. Bogaerts, 2006. "Transient analysis of a wastewater treatment biofilter -- distributed parameter modelling and state estimation," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 12(5), pages 423-440, October.
    2. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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