Title: A feedback control law to stabilise a harvested fish population system

Authors: E. El Mazoudi, N. Elalami, A. Ouahbi

Addresses: Laboratoire de Recherche en Economie de l'Energie, Environnement et Ressources, Departement d'Economie, University Caddy Ayyad, Marrakech, Maroc; Laboratoire d'Automatique et Informatique Industrielle, Ecole Mohammadia d'ingenieurs, Avenue Ibsina 765, Agdal Rabat, Maroc. ' Laboratoire d'Automatique et Informatique Industrielle, Ecole Mohammadia d'ingenieurs, Avenue Ibsina 765, Agdal Rabat, Maroc. ' Institut Superieur de Technologie Appliquee, ZI B.P 399, Settat, Maroc

Abstract: In this paper, we consider the problem of stabilising a continuous fish population system via a state feedback control. The model considered is structured in n age classes and includes a non-linear stock-recruitment relationship. In our case, the variation of the fishing effort is used as a control term, the age classes as states and the quantity of captured fish per unit of effort as a measured output. The back stepping approach is employed to stabilise the studied system around a reference equilibrium point. Explicit expression of a bounded fishing effort and a Lyapunov function are given. An example is tested to illustrate the applicability of the proposed technique.

Keywords: age structured modelling; feedback control; stabilisation; back stepping; fish population stability; harvested fish; fish catch.

DOI: 10.1504/IJMIC.2011.040078

International Journal of Modelling, Identification and Control, 2011 Vol.12 No.4, pp.341 - 347

Published online: 21 Mar 2015 *

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