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.
Highlights
The problem of natural stock management has received great attention during the last decades
We show how to apply this theory to address the stock estimation problem for an exploited fish population
The goal of this paper is to give a simple tool that would allow us to give a dynamical estimation of the state (x1(k), . . . , xn(k)) of the stock using the available information which is the value of the captures
Summary
The problem of natural stock management has received great attention during the last decades. Developers of management policies in the exploitation of renewable resource stocks need to have a good estimate of the available resource. Current mathematical models together with computer simulations are useful in describing the evolution of complex systems. One of the important problems in control theory is to reconcile the available data with the used mathematical model. This problem is known as the observability problem, and it is. Primary: 34D23, 92D25, 93B07, 93C10, 93C41; Secondary: 93B50
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