Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction

Sivakumar Pitchaiah, Antonios Armaou

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

3 Citations (Scopus)

Abstract

This work addresses the problem of tracking and stabilization of FitzHugh-Nagumo equation (FHN) subject to Neumann boundary conditions via static output feedback control using adaptive model reduction methodology and specifically the adaptive proper orthogonal decomposition (APOD) approach. Initially, an ensemble of eigenfunctions is constructed based on a relatively small data ensemble using method of snapshots and Karhunen-Lòeve expansions (KLE). We then recursively update the eigenfunctions as additional data from the process become available periodically, thus relaxing the need for a representative ensemble in KLE. An accurate reduced-order model (ROM) is constructed and periodically refined via nonlinear Galerkin's method based on the eigenfunctions. Using the ROM and continuous measurements available from restricted number of sensors a static output feedback controller is subsequently designed. This controller is used achieve the desired control objective of stabilizing the FHN equation at a desired reference trajectory. The success of the adaptive model reduction and output-feedback controller design methodology are illustrated using computer simulations.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages864-869
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

FitzHugh-Nagumo Equations
Output Feedback Control
Model Reduction
Feedback control
Eigenfunctions
Static Output Feedback
Reduced Order Model
Eigenvalues and eigenfunctions
Ensemble
Nonlinear Galerkin Method
Controllers
Controller
Ensemble Methods
Orthogonal Decomposition
Snapshot
Output Feedback
Neumann Boundary Conditions
Feedback
Controller Design
Design Methodology

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Pitchaiah, S., & Armaou, A. (2010). Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 864-869). [5717497] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717497
Pitchaiah, Sivakumar ; Armaou, Antonios. / Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 864-869 (Proceedings of the IEEE Conference on Decision and Control).
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Pitchaiah, S & Armaou, A 2010, Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717497, Proceedings of the IEEE Conference on Decision and Control, pp. 864-869, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717497

Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. / Pitchaiah, Sivakumar; Armaou, Antonios.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 864-869 5717497 (Proceedings of the IEEE Conference on Decision and Control).

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

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Pitchaiah S, Armaou A. Output feedback control of the FitzHugh-Nagumo equation using adaptive model reduction. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 864-869. 5717497. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717497