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

Ivan Francisco Yupanqui Tello, Alain Vande Wouwer and Daniel Coutinho
Additional contact information
Ivan Francisco Yupanqui Tello: Systems, Estimation, Control, and Optimization (SECO), University of Mons, 7000 Mons, Belgium
Alain Vande Wouwer: Systems, Estimation, Control, and Optimization (SECO), University of Mons, 7000 Mons, Belgium
Daniel Coutinho: Postgraduate Program in Engineering of Automation and Systems, Federal University of Santa Catarina, Florianopolis 88040-900, SC, Brazil

Mathematics, 2021, vol. 9, issue 24, 1-15

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.

Keywords: distributed parameter systems; partial differential equations; observers; state estimation; monitoring; early lumping; late lumping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3180/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3180/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:24:p:3180-:d:698872

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().