Dynamic observers for unknown populations

Guiver, Chris; Poppelreiter, Nathan; Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

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.

• Journal Article Type: Article
• Acceptance Date: Jun 15, 2020
• Publication Date: 2021-06
• Deposit Date: Jul 24, 2020
• Publicly Available Date: Jan 1, 2022
• Journal: Discrete and Continuous Dynamical Systems - Series B
• Print ISSN: 1531-3492
• Publisher: American Institute of Mathematical Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 6
• Pages: 3279-3302
• DOI: https://doi.org/10.3934/dcdsb.2020232
• Keywords: adaptive management, dynamic observer, input-to-state stability, Lur’e system, population ecology, positive system
• Public URL: http://researchrepository.napier.ac.uk/Output/2677246