Monitoring and Control in a Spatially Structured Population Model

In the paper methods of Mathematical Systems Theory are applied to the dynamical analysis of a harvested population with a reserve area. Although the methodology also applies to rather general spatially structured populations, for a concrete interpretation, we consider a fish population living in a free fishing area and in a reserved area, with migration between them. Using a fishing effort model based on logistic growth in both areas, from the catch, by the construction of an auxiliary system called observer, we dynamically estimate the total fish stock. A similar method also applies to the case of a changing environment, when there is a time-dependent abiotic environmental effect described by an additional exosystem. Furthermore, we also consider the problem of steering the population into a desired new equilibrium. To this end an optimal control problem is set up, which is numerically solved using an optimal control toolbox developed for MatLab.