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

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.

Low-Gain Integral Control for Multi-Input Multioutput Linear Systems With Input Nonlinearities

“…Finally, the results reported here extend, generalise and refine those in [29] where, in the context of ecological management, low-gain PI control of linear discrete-time positive systems (see, for example, [30], [31]) subject to input saturation is considered.…”

Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

“…In closing, we comment that the previous works 42,43 by the current authors have considered the utility of low‐gain integral control for population management of linear models arising in theoretical ecology, as a potential tool for population conservation. However, linear models allow for unbounded, exponential growth which is not ecologically realistic and, in fact, nonlinear systems of Lur'e type are known to arise naturally in this setting; see, for example Reference 44.…”

Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities

“…In much of the literature which addresses the low-gain integral control problem in the presence of nonlinearities (see, for example, [5,6,9,10,11,19]), attention is restricted to single-input single-output systems. To the best of our knowledge, the only exceptions are [15,16] which develop low-gain integral control schemes for multi-input multi-output linear finite-dimensional systems with input nonlinearities. In contrast to [5,6,9,10,11,19], the low-gain integral controllers presented in [15,16] include anti-windup components.…”

“…To the best of our knowledge, the only exceptions are [15,16] which develop low-gain integral control schemes for multi-input multi-output linear finite-dimensional systems with input nonlinearities. In contrast to [5,6,9,10,11,19], the low-gain integral controllers presented in [15,16] include anti-windup components. We remark that integrator windup can cause performance and/or stability degradation in integral control systems subject to input saturation.…”

“…We remark that integrator windup can cause performance and/or stability degradation in integral control systems subject to input saturation. Indeed, as [15,Example 10] shows, in the absence of any anti-windup component, the integrator state for the multivariable low-gain integral control scheme considered in [15,16] may be unbounded. The theory of anti-windup control seeks to avoid or reduce integrator windup and is a much researched area, we only mention the references [1,2,12,28] which provide a small sample of the available literature.…”