Using spatial H2 norm for sensor placement in parabolic partial differential equations

Antonios Armaou, Michael A. Demetriou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

The issue of optimal sensor placement in the presence of disturbance is investigated for a class of transport-reaction processes, mathematically modeled by linear parabolic partial differential equations. Specifically, using modal decomposition to discretize the spatial coordinate, the optimal sensor location is computed through the solution of a nonlinear optimization problem in appropriate L2 space. The notions of spatial and modal observability and robustness index are employed for the definition of the objective and constraint functionals. The formulated problem is subsequently solved using standard search algorithms. The proposed method is illustrated on a representative thermal diffusion process modeled by a one-dimensional parabolic PDE, where, in the presence of disturbances with known distribution, the optimal location of a single point sensor is computed.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
Pages1467-1472
Number of pages6
StatePublished - Dec 1 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Other

Other2006 American Control Conference
CountryUnited States
CityMinneapolis, MN
Period6/14/066/16/06

Fingerprint

Partial differential equations
Sensors
Thermal diffusion
Observability
Robustness (control systems)
Decomposition

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Armaou, A., & Demetriou, M. A. (2006). Using spatial H2 norm for sensor placement in parabolic partial differential equations. In Proceedings of the 2006 American Control Conference (pp. 1467-1472). [1656425] (Proceedings of the American Control Conference; Vol. 2006).
Armaou, Antonios ; Demetriou, Michael A. / Using spatial H2 norm for sensor placement in parabolic partial differential equations. Proceedings of the 2006 American Control Conference. 2006. pp. 1467-1472 (Proceedings of the American Control Conference).
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Armaou, A & Demetriou, MA 2006, Using spatial H2 norm for sensor placement in parabolic partial differential equations. in Proceedings of the 2006 American Control Conference., 1656425, Proceedings of the American Control Conference, vol. 2006, pp. 1467-1472, 2006 American Control Conference, Minneapolis, MN, United States, 6/14/06.

Using spatial H2 norm for sensor placement in parabolic partial differential equations. / Armaou, Antonios; Demetriou, Michael A.

Proceedings of the 2006 American Control Conference. 2006. p. 1467-1472 1656425 (Proceedings of the American Control Conference; Vol. 2006).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Armaou A, Demetriou MA. Using spatial H2 norm for sensor placement in parabolic partial differential equations. In Proceedings of the 2006 American Control Conference. 2006. p. 1467-1472. 1656425. (Proceedings of the American Control Conference).