Dynamic observers for unknown populations

Christopher Guiver, Nathan Poppelreiter, Richard Rebarber, Brigitte Tenhumberg, Stuart Townley

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Abstract

Dynamic observers are considered in the context of structured-population modeling and management. Roughly, observers combine a known measured variable of some process with a model of that process to asymptotically reconstruct the unknown state variable of the model. We investigate the potential use of observers for reconstructing population distributions described by density-independent (linear) models and a class of density-dependent (nonlinear) models. In both the density-dependent and -independent cases, we show, in several ecologically reasonable circumstances, that there is a natural, optimal construction of these observers. Further, we describe the robustness these observers exhibit with respect to disturbances and uncertainty in measurement.

Original languageEnglish
Pages (from-to)3279-3302
Number of pages24
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume26
Issue number6
DOIs
Publication statusPublished - 30 Jun 2021

Bibliographical note

Funding Information:
Acknowledgments. Chris Guiver and Stuart Townley’s contribution to this work was partially supported by the UK EPSRC grant EP/I019456/1. Nathan Poppel-reiter and Richard Rebarber’s contribution to this work was partially supported by NSF Grant DMS-1412598. Brigitte Tenhumberg’s contribution was partially supported by NSF Grant DEB 1655117 and USDA/NIFA Grant 2017-03807.

Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Adaptive management
  • Dynamic observer
  • Input-to-state stability
  • Lur'e system
  • Population ecology
  • Positive system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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