On the stock estimation for some fishery systems
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In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation \(\hat x(t)\) of the unmeasurable stock state x(t). Moreover the convergence speed of \(\hat x(t)\) towards x(t) can be chosen.
KeywordsFishery models Stage-structured population models Estimation Harvested fish population Observers
We thank the anonymous referees for their valuable comments and suggestions that have helped us to improve the presentation of this article.
- Bornard G, Hammouri H (1991) A high gain observer for a class of uniformly observable systems. Proceedings of the 30th IEEE conference on decision and control, vol 2, pp 1494–1496, December 1991Google Scholar
- Clark CW (1990) Mathematical bioeconomics. The optimal management of renewable resources, 2nd edn. Wiley-Interscience Publication, New YorkGoogle Scholar
- Gauthier JP, Kupka I (2001) Deterministic observation theory and applications. Cambridge University Press, CambridgeGoogle Scholar
- Guiro A, Iggidr A, Ngom D, Touré H (2008) A non linear observer for a fishery model. In: Proceedings of 17th Triennial IFAC World Congress, Seoul, Korea, July 6–11, 2008Google Scholar
- Gulland JA (1983) Fish stock assessment, a manual of basic methods. Wiley, ChichesterGoogle Scholar
- Iggidr A (2004) Controllability, observability and stability of mathematical models, in Mathematical Models. In: Filar JA (ed) Encyclopedia of life support systems (EOLSS). Developed under the auspices of the UNESCO, Eolss Publishers, Oxford, UK. http://www.eolss.net. Retrieved 31 Jan 2006
- Iggidr A, Sallet G (1993) Exponential stabilization of nonlinear systems by an estimated state feedback. In: Proceedings of the 2nd European control conference ECC’93. Groningen, Pays-BasGoogle Scholar
- Isidori A (1995) Nonlinear control systems, 3rd edn. Communications and Control Engineering Series. Springer, BerlinGoogle Scholar
- Sontag ED (1998) Mathematical control theory. Deterministic finite-dimensional systems, volume 6 of Texts in applied mathematics. Springer-Verlag, New YorkGoogle Scholar
- Tornambe A (1989) Use of asymptotic observers having-high-gains in the state and parameter estimation. Proceedings of the 28th IEEE conference on decision and control, vol 2, pp 1791–1794, December 1989Google Scholar
- Touzeau S (1997) Modèles de contrôle en gestion des pêches. Thesis, University of Nice-Sophia Antipolis, FranceGoogle Scholar