Robust set-point regulation for ecological models with multiple management goals

Guiver, Chris; Mueller, Markus; Hodgson, Dave; Townley, Stuart

Abstract

Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.

Citation

Guiver, C., Mueller, M., Hodgson, D., & Townley, S. (2016). Robust set-point regulation for ecological models with multiple management goals. Journal of Mathematical Biology, 72, 1467-1529. https://doi.org/10.1007/s00285-015-0919-7

• Journal Article Type: Article
• Acceptance Date: Jul 25, 2015
• Online Publication Date: Aug 5, 2015
• Publication Date: 2016-05
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Aug 5, 2020
• Journal: Journal of Mathematical Biology
• Print ISSN: 0303-6812
• Publisher: BMC
• Peer Reviewed: Peer Reviewed
• Volume: 72
• Pages: 1467-1529
• DOI: https://doi.org/10.1007/s00285-015-0919-7
• Keywords: Anti-windup control, PI control, Population ecology, Positive state system, Resource management
• Public URL: http://researchrepository.napier.ac.uk/Output/2677323