An observer for a nonlinear age-structured model of a harvested fish population
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1.
Laboratoire d’Analyse Numérique et d’Informatique (LANI), UFR de Sciences Appliquées et de Technologie., Université Gaston Berger. B.P. 234 Saint-Louis,
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INRIA-Lorraine and University Paul Verlaine-Metz, LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy, 57045 Metz Cedex 01
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3.
Laboratoire d’Analyse Mathématique des Equations (LAME), Faculté des Sciences et Techniques. Université de Ouagadougou, B.P. 7021 Ouagadougou,
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4.
ISTA/ZI, B.P 399, Settat, Maroc
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Received:
01 June 2007
Accepted:
29 June 2018
Published:
01 March 2008
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MSC :
Primary: 34D23, 92D25,93B07, 93C10, 93C41; Secondary: 93B50.
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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[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 337-354. doi: 10.3934/mbe.2008.5.337
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Abstract
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.
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