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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 2: 337-354. doi: 10.3934/mbe.2008.5.337
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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,
  • 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,
  • 4.
    ISTA/ZI, B.P 399, Settat, Maroc
  • Received: 01 June 2007 Accepted: 29 June 2018 Published: 01 March 2008

  • MSC : Primary: 34D23, 92D25,93B07, 93C10, 93C41; Secondary: 93B50.

  • 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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  • 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.


  • This article has been cited by:

    1. Xinyuan Liao, Yuming Chen, Shengfan Zhou, Traveling wavefronts of a prey–predator diffusion system with stage-structure and harvesting, 2011, 235, 03770427, 2560, 10.1016/j.cam.2010.11.008
    2. A. Guiro, A. Iggidr, D. Ngom, H. Touré, On the stock estimation for some fishery systems, 2009, 19, 0960-3166, 313, 10.1007/s11160-009-9104-7
    3. M. S. Vinogradova, S. B. Tkachev, O. S. Tkacheva, Using an Observer in a Sliding Mode for Modeling Antiangiogenic Therapy, 2019, 2412-5911, 52, 10.24108/mathm.0618.0000165
    4. Aboudramane Guiro, Abderrahman Iggidr, Diène Ngom, On the Stock Estimation for a Harvested Fish Population, 2012, 74, 0092-8240, 116, 10.1007/s11538-011-9667-z
    5. A. A. Kaddour, El Houssine El Mazoudi, N. Elalami, 2011, Multimodel software sensor for a harvested fish population system, 978-0-9567157-0-8, 240, 10.1109/ICMIC.2011.5973708
    6. Achraf Ait Kaddour, Khalid Benjelloun, Noureddine Elalami, El Houssine El Mazoudi, Multimodel robust observer for an uncertain fish population model, 2014, 256, 00255564, 79, 10.1016/j.mbs.2014.07.004
    7. Inmaculada López, Zoltán Varga, Manuel Gámez, József Garay, Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment, 2022, 10, 2227-7390, 2707, 10.3390/math10152707
    8. Aboudramane Guiro, Dramane Ouedraogo, Harouna Ouedraogo, 2023, Chapter 10, 978-3-031-27660-6, 259, 10.1007/978-3-031-27661-3_10
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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