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

Diène Ngom (1) , Abderrahman Iggidr (2) , Aboudramane Guiro (3) , Abderrahim Ouahbi (4)

1 LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal]
2 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
3 LAME - Laboratoire d'Analyse Mathématique des Equations
4 ISTA - Institut Spécialisé de Technologie Appliquée

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.

Mots clés: Discrete time system; Age structured population models; Estimation; Harvested fish population; Observers.; Observers

Domaines: Systèmes dynamiques [math.DS]; Sciences et techniques des pêches

Diène Ngom, Abderrahman Iggidr, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear age-structured model of a harvested fish population.. Mathematical Biosciences and Engineering, 2008, 5 (2), pp.337-354. ⟨inria-00551871⟩