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Adaptive Control Based Harvesting Strategy for a Predator–Prey Dynamical System

Adaptive Control Based Harvesting Strategy for a Predator–Prey Dynamical System This paper deals with designing a harvesting control strategy for a predator–prey dynamical system, with parametric uncertainties and exogenous disturbances. A feedback control law for the harvesting rate of the predator is formulated such that the population dynamics is asymptotically stabilized at a positive operating point, while maintaining a positive, steady state harvesting rate. The hierarchical block strict feedback structure of the dynamics is exploited in designing a backstepping control law, based on Lyapunov theory. In order to account for unknown parameters, an adaptive control strategy has been proposed in which the control law depends on an adaptive variable which tracks the unknown parameter. Further, a switching component has been incorporated to robustify the control performance against bounded disturbances. Proofs have been provided to show that the proposed adaptive control strategy ensures asymptotic stability of the dynamics at a desired operating point, as well as exact parameter learning in the disturbance-free case and learning with bounded error in the disturbance prone case. The dynamics, with uncertainty in the death rate of the predator, subjected to a bounded disturbance has been simulated with the proposed control strategy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Adaptive Control Based Harvesting Strategy for a Predator–Prey Dynamical System

Acta Biotheoretica , Volume 66 (4) – Apr 23, 2018

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References (39)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-018-9323-1
Publisher site
See Article on Publisher Site

Abstract

This paper deals with designing a harvesting control strategy for a predator–prey dynamical system, with parametric uncertainties and exogenous disturbances. A feedback control law for the harvesting rate of the predator is formulated such that the population dynamics is asymptotically stabilized at a positive operating point, while maintaining a positive, steady state harvesting rate. The hierarchical block strict feedback structure of the dynamics is exploited in designing a backstepping control law, based on Lyapunov theory. In order to account for unknown parameters, an adaptive control strategy has been proposed in which the control law depends on an adaptive variable which tracks the unknown parameter. Further, a switching component has been incorporated to robustify the control performance against bounded disturbances. Proofs have been provided to show that the proposed adaptive control strategy ensures asymptotic stability of the dynamics at a desired operating point, as well as exact parameter learning in the disturbance-free case and learning with bounded error in the disturbance prone case. The dynamics, with uncertainty in the death rate of the predator, subjected to a bounded disturbance has been simulated with the proposed control strategy.

Journal

Acta BiotheoreticaSpringer Journals

Published: Apr 23, 2018

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