Simple adaptive control for positive linear systems with applications to pest management

Chris Guiver, Christina Edholm, Yu Jin, Markus Mueller, Jim Powell, Richard Rebarber, Brigitte Tenhumberg, Stuart Townley

Research output: Contribution to journalArticle

  • 2 Citations

Abstract

Pest management is vitally important for modern arable farming, but models for pest species are often highly uncertain. In the context of pest management, control actions are naturally described by a nonlinear feedback that is generally unknown, which thus motivates a robust control approach. We argue that adaptive approaches are well suited for the management of pests and propose a simple high-gain adaptive tuning mechanism so that the nonlinear feedback achieves exponential stabilization. Furthermore, a switched adaptive controller is proposed, cycling through a set of given control actions, that also achieves global asymptotic stability. Such a model in practice allows for the possibility of rotating between different courses of management action. In developing our control strategies we appeal to comparison and monotonicity arguments. Interestingly, componentwise nonnegativity of the model, combined with an irreducibility assumption, implies that several issues typically associated with high-gain adaptive controllers do not arise and usual high-gain structural assumptions are not required.

LanguageEnglish
Pages238-275
Number of pages38
JournalSIAM Journal on Applied Mathematics
Volume76
Issue number1
DOIs
StatusPublished - 2016

Fingerprint

Positive Systems
Adaptive Control
Linear systems
Linear Systems
Nonlinear feedback
Exponential Stabilization
Controller
Controllers
Feedback Stabilization
Irreducibility
Nonnegativity
Appeal
Global Asymptotic Stability
Cycling
Robust control
Asymptotic stability
Robust Control
Monotonicity
Control Strategy
Tuning

Keywords

  • Adaptive control
  • High-gain control
  • Pest management
  • Positive state linear system

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Guiver, C., Edholm, C., Jin, Y., Mueller, M., Powell, J., Rebarber, R., ... Townley, S. (2016). Simple adaptive control for positive linear systems with applications to pest management. SIAM Journal on Applied Mathematics, 76(1), 238-275. DOI: 10.1137/140996926

Simple adaptive control for positive linear systems with applications to pest management. / Guiver, Chris; Edholm, Christina; Jin, Yu; Mueller, Markus; Powell, Jim; Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart.

In: SIAM Journal on Applied Mathematics, Vol. 76, No. 1, 2016, p. 238-275.

Research output: Contribution to journalArticle

Guiver, C, Edholm, C, Jin, Y, Mueller, M, Powell, J, Rebarber, R, Tenhumberg, B & Townley, S 2016, 'Simple adaptive control for positive linear systems with applications to pest management' SIAM Journal on Applied Mathematics, vol 76, no. 1, pp. 238-275. DOI: 10.1137/140996926
Guiver C, Edholm C, Jin Y, Mueller M, Powell J, Rebarber R et al. Simple adaptive control for positive linear systems with applications to pest management. SIAM Journal on Applied Mathematics. 2016;76(1):238-275. Available from, DOI: 10.1137/140996926
Guiver, Chris ; Edholm, Christina ; Jin, Yu ; Mueller, Markus ; Powell, Jim ; Rebarber, Richard ; Tenhumberg, Brigitte ; Townley, Stuart. / Simple adaptive control for positive linear systems with applications to pest management. In: SIAM Journal on Applied Mathematics. 2016 ; Vol. 76, No. 1. pp. 238-275
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