A switching feedback control approach for persistence of managed resources

Franco, Daniel; Guiver, Chris; Smith, Phoebe; Townley, Stuart

Abstract

An adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations. In overview, the objective is to choose a control strategy which ensures persistence of the state, consequently avoiding zero which corresponds to absence or extinction. A robust feedback control solution is proposed as the effects of different management actions are assumed to be uncertain. Our motivating application is to the conservation of dynamic resources, such as populations, which are naturally positive quantities and where discrete and distinct courses of management actions, or control strategies, are available. The theory is illustrated with examples from population ecology.

Citation

Franco, D., Guiver, C., Smith, P., & Townley, S. (2022). A switching feedback control approach for persistence of managed resources. Discrete and Continuous Dynamical Systems - Series B, 27(3), 1765-1787. https://doi.org/10.3934/dcdsb.2021109

• Journal Article Type: Article
• Acceptance Date: Mar 4, 2021
• Publication Date: 2022-03
• Deposit Date: Mar 6, 2021
• Publicly Available Date: May 1, 2022
• Print ISSN: 1531-3492
• Publisher: American Institute of Mathematical Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 3
• Pages: 1765-1787
• DOI: https://doi.org/10.3934/dcdsb.2021109
• Keywords: Conservation, feedback control, mathematical ecology, resource management, positive system, simple adaptive control
• Public URL: http://researchrepository.napier.ac.uk/Output/2750032