Dynamic observers for unknown populations

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

doi:10.3934/dcdsb.2020232

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 language	English
Pages (from-to)	3279-3302
Number of pages	24
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	26
Issue number	6
DOIs	https://doi.org/10.3934/dcdsb.2020232
Publication status	Published - 30 Jun 2021

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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10.3934/dcdsb.2020232

2020_05_31_observers.pdf
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Dynamical Continuous Systems - B following peer review. The definitive publisher-authenticated versionChris Guiver, Nathan Poppelreiter, Richard Rebarber, Brigitte Tenhumberg, Stuart Townley. Dynamic observers for unknown populations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3279-3302 is available online at: http://dx.doi.org/10.3934/dcdsb.2020232
Accepted author manuscript, 379 KBLicence: Unspecified

Cite this

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title = "Dynamic observers for unknown populations",

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.",

keywords = "Adaptive management, Dynamic observer, Input-to-state stability, Lur'e system, Population ecology, Positive system",

author = "Christopher Guiver and Nathan Poppelreiter and Richard Rebarber and Brigitte Tenhumberg and Stuart Townley",

note = "Funding Information: Acknowledgments. Chris Guiver and Stuart Townley{\textquoteright}s contribution to this work was partially supported by the UK EPSRC grant EP/I019456/1. Nathan Poppel-reiter and Richard Rebarber{\textquoteright}s contribution to this work was partially supported by NSF Grant DMS-1412598. Brigitte Tenhumberg{\textquoteright}s contribution was partially supported by NSF Grant DEB 1655117 and USDA/NIFA Grant 2017-03807. Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved.",

year = "2021",

month = jun,

day = "30",

doi = "10.3934/dcdsb.2020232",

language = "English",

volume = "26",

pages = "3279--3302",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

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TY - JOUR

T1 - Dynamic observers for unknown populations

AU - Guiver, Christopher

AU - Poppelreiter, Nathan

AU - Rebarber, Richard

AU - Tenhumberg, Brigitte

AU - Townley, Stuart

N1 - 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.

PY - 2021/6/30

Y1 - 2021/6/30

N2 - 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.

AB - 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.

KW - Adaptive management

KW - Dynamic observer

KW - Input-to-state stability

KW - Lur'e system

KW - Population ecology

KW - Positive system

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DO - 10.3934/dcdsb.2020232

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SN - 1531-3492

VL - 26

SP - 3279

EP - 3302

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 6

ER -

Dynamic observers for unknown populations

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Nonlinear Feedback Loops and Robustness in Modelling Biological Invasions

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Dynamic observers for unknown populations

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Nonlinear Feedback Loops and Robustness in Modelling Biological Invasions

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