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2008, 5(2): 337-354. doi: 10.3934/mbe.2008.5.337

An observer for a nonlinear age-structured model of a harvested fish population

1. 

Laboratoire d’Analyse Numérique et d’Informatique (LANI), UFR de Sciences Appliquées et de Technologie., Université Gaston Berger. B.P. 234 Saint-Louis,, Senegal

2. 

INRIA-Lorraine and University Paul Verlaine-Metz, LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy, 57045 Metz Cedex 01

3. 

Laboratoire d’Analyse Mathématique des Equations (LAME), Faculté des Sciences et Techniques. Université de Ouagadougou, B.P. 7021 Ouagadougou,, Burkina Faso

4. 

ISTA/ZI, B.P 399, Settat, Maroc, Morocco

Received  June 2007 Revised  January 2008 Published  March 2008

We consider an age-structured model of a harvested population. This model is a discrete-time system that includes a nonlinear stock-recruitment relationship. Our purpose is to estimate the stock state. To achieve this goal, we built an observer, which is an auxiliary system that uses the total number of fish caught over each season and gives a dynamical estimation of the number of fish by age class. We analyse the convergence of the observer and we show that the error estimation tends to zero with exponential speed if a condition on the fishing effort is satisfied. Moreover the constructed observer (dynamical estimator) does not depend on the poorly understood stock-recruitment relationship. This study shows how some tools from nonlinear control theory can help to deal with the state estimation problem in the field of renewable resource management.
Citation: Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear age-structured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337-354. doi: 10.3934/mbe.2008.5.337
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