Stabilisation by adaptive feedback control for positive difference equations with applications in pest management

Edholm, Christina; Guiver, Chris; Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

Abstract

An adaptive feedback control scheme is proposed for stabilising a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers, and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples.

• Journal Article Type: Article
• Acceptance Date: Mar 20, 2022
• Online Publication Date: Jul 28, 2022
• Publication Date: 2022-08
• Deposit Date: Mar 21, 2022
• Publicly Available Date: Mar 21, 2022
• Journal: SIAM Journal on Control and Optimization
• Print ISSN: 0363-0129
• Electronic ISSN: 1095-7138
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 60
• Issue: 4
• Pages: 2214-2245
• DOI: https://doi.org/10.1137/21m1398240
• Keywords: feedback control, mathematical ecology, Lur’e system, pest and weed management, positive system, simple adaptive control
• Public URL: http://researchrepository.napier.ac.uk/Output/2856399
• Publisher URL: https://www.siam.org/publications/journals/siam-journal-on-control-and-optimization-sicon