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.
Highlights
Regulation by feedback arises in numerous areas of science and engineering; such as acoustics, electrical circuits, aviation and biological systems
The motivation for the current study is twofold: first, to further explore the utility of feedback control in ecological management type problems, and it is in this context that we have posed much of the present material and our examples
The second purpose is to further develop the suite of robust feedback control for positive state systems—models that arise in a variety of other physically and biologically motivated scenarios
Summary
Regulation by feedback arises in numerous areas of science and engineering; such as acoustics, electrical circuits, aviation and biological systems. The application of PI control to the above multi-objective management problem is novel itself and, we believe, a useful and timely contribution to the suite of tools available to population managers, conservation biologists and other end users To present such a solution requires new mathematical results in control theory for two reasons. The key difference between the present contribution and Guiver et al (2015) is that in the latter we restricted attention to m = p = 1 but here the situation m, p > 1 is permitted, implying that numerous measurements are recorded and management actions taken—so-called management with multiple goals in ecological terminology or the multi-input, multi-output case in control theoretic terminology. Techniques from optimal control have appeared extensively in the mathematical ecology, conservation and resource management literature where an input to a control system denotes a management strategy that is applied to a ecological process, such as a modelled population. Recall that proofs of all novel stated results are contained in “Appendix C”
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