Search Advanced

Mathematical Biosciences and Engineering

2008, Volume 5, Issue 2: 337-354. doi: 10.3934/mbe.2008.5.337
Previous Article Next Article

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

    Related Papers:

    [1] AIMS Energy Editorial Office . Retraction: Salah A.M. Elmoselhy. Validated analytical modelling of frequency-based aspects, eccentricity and stress concentration in diesel engines with flexible crankshaft. AIMS Energy, 2018, 6(6): 1050-1066. doi: 10.3934/energy.2018.6.1050. AIMS Energy, 2019, 7(3): 349-349. doi: 10.3934/energy.2019.349
    [2] Sunbong Lee, Shaku Tei, Kunio Yoshikawa . Properties of chicken manure pyrolysis bio-oil blended with diesel and its combustion characteristics in RCEM, Rapid Compression and Expansion Machine. AIMS Energy, 2014, 2(3): 210-218. doi: 10.3934/energy.2014.3.210
    [3] Saad S. Alrwashdeh . Investigation of the effect of the injection pressure on the direct-ignition diesel engine performance. AIMS Energy, 2022, 10(2): 340-355. doi: 10.3934/energy.2022018
    [4] Tien Duy Nguyen, Trung Tran Anh, Vinh Tran Quang, Huy Bui Nhat, Vinh Nguyen Duy . An experimental evaluation of engine performance and emissions characteristics of a modified direct injection diesel engine operated in RCCI mode. AIMS Energy, 2020, 8(6): 1069-1087. doi: 10.3934/energy.2020.6.1069
    [5] Abshir Ashour, Taib Iskandar Mohamad, Kamaruzzaman Sopian, Norasikin Ahmad Ludin, Khaled Alzahrani, Adnan Ibrahim . Performance optimization of a photovoltaic-diesel hybrid power system for Yanbu, Saudi Arabia. AIMS Energy, 2021, 9(6): 1260-1273. doi: 10.3934/energy.2021058
    [6] Sanaur Rehman, Shah Shahood Alam . Combustion and soot formation characteristics of homogeneous supercritical sprays of dieseline blend in constant volume chamber. AIMS Energy, 2020, 8(5): 959-987. doi: 10.3934/energy.2020.5.959
    [7] Lin Dong, Michael Grissom, Frank T. Fisher . Resonant frequency of mass-loaded membranes for vibration energy harvesting applications. AIMS Energy, 2015, 3(3): 344-359. doi: 10.3934/energy.2015.3.344
    [8] Girma Misrak, Molina Marta, Assefa Abebayehu . Feasibility study of a wind powered water pumping system for rural Ethiopia. AIMS Energy, 2015, 3(4): 851-868. doi: 10.3934/energy.2015.4.851
    [9] Simona Silvia Merola, Luca Marchitto, Cinzia Tornatore, Gerardo Valentino . Spray-combustion process characterization in a common rail diesel engine fuelled with butanol-diesel blends by conventional methods and optical diagnostics. AIMS Energy, 2014, 2(2): 116-132. doi: 10.3934/energy.2014.2.116
    [10] Mulualem T. Yeshalem, Baseem Khan . Design of an off-grid hybrid PV/wind power system for remote mobile base station: A case study. AIMS Energy, 2017, 5(1): 96-112. doi: 10.3934/energy.2017.1.96
  • 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.


    The status of this article has been Retraction: AIMS Energy 2019, Volume 7, Issue 3: 349-349. doi: 10.3934/energy.2019.349

  • This article has been cited by:

    1. AIMS Energy Editorial Office, Retraction: Salah A.M. Elmoselhy. Validated analytical modelling of frequency-based aspects, eccentricity and stress concentration in diesel engines with flexible crankshaft. AIMS Energy, 2018, 6(6): 1050–1066. doi: 10.3934/energy.2018.6.1050, 2019, 7, 2333-8334, 349, 10.3934/energy.2019.349
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2671) PDF downloads(505) Cited by(8)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog