Open AccessA switching feedback control approach for persistence of managed resources
Author(s) -
Daniel Franco,
Christopher Guiver,
Phoebe Smith,
Stuart Townley
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021109
Subject(s) - persistence (discontinuity) , control theory (sociology) , feedback control , control (management) , zero (linguistics) , extinction (optical mineralogy) , adaptive control , population , computer science , state (computer science) , mathematics , mathematical optimization , control engineering , engineering , algorithm , artificial intelligence , physics , demography , linguistics , philosophy , geotechnical engineering , optics , sociology
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.