### 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.

Language | English |
---|---|

Pages | 1467-1529 |

Number of pages | 63 |

Journal | Journal of Mathematical Biology |

Volume | 72 |

Issue number | 6 |

DOIs | |

Status | Published - 1 May 2016 |

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### Keywords

- Anti-windup control
- PI control
- Population ecology
- Positive state system
- Resource management

### Cite this

*Journal of Mathematical Biology*,

*72*(6), 1467-1529. DOI: 10.1007/s00285-015-0919-7

**Robust set-point regulation for ecological models with multiple management goals.** / Guiver, Chris; Mueller, Markus; Hodgson, Dave; Townley, Stuart.

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol 72, no. 6, pp. 1467-1529. DOI: 10.1007/s00285-015-0919-7

}

TY - JOUR

T1 - Robust set-point regulation for ecological models with multiple management goals

AU - Guiver,Chris

AU - Mueller,Markus

AU - Hodgson,Dave

AU - Townley,Stuart

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Anti-windup control

KW - PI control

KW - Population ecology

KW - Positive state system

KW - Resource management

UR - http://www.scopus.com/inward/record.url?scp=84938704796&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s00285-015-0919-7

UR - http://dx.doi.org/10.1007/s00285-015-0919-7

U2 - 10.1007/s00285-015-0919-7

DO - 10.1007/s00285-015-0919-7

M3 - Article

VL - 72

SP - 1467

EP - 1529

JO - Journal of Mathematical Biology

T2 - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6

ER -