An observer for a nonlinear age-structured model of a harvested fish population - Diène Ngom; A. Iggidir; Aboudramane Guiro; Abderrahim Ouahbi (Mathematical Biosciences and Engineering)
We consider an age-structured model of a harvested population.This model is a discrete-time system that includes a nonlinear stock-recruitmentrelationship. 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 numberof fish caught over each season and gives a dynamical estimation of the numberof fish by age class. We analyse the convergence of the observer and we showthat the error estimation tends to zero with exponential speed if a conditionon the fishing effort is satisfied. Moreover the constructed observer (dynamicalestimator) does not depend on the poorly understood stock-recruitmentrelationship. This study shows how some tools from nonlinear control theorycan help to deal with the state estimation problem in the field of renewableresource management.