Abstract
Issues related to the implementation of dynamic programming for optimal control of a three-dimensional dynamic model (the fish populations management problem) are presented. They belong to a class of models called Lotka-Volterra models. The existence of bionomic equilibria will be considered. The problem of optimal harvest policy is then solved for the control of various classes of its behaviour. Therefore the focus will be the optimality conditions by using the Bellman principle. Moreover, we consider a different form for the optimal value of the control vector, namely the feedback or closed-loop form of the control. Academic examples are studied in order to demonstrate the proposed methods.
Highlights
Issues related to the implementation of dynamic programming for optimal control of a three-dimensional dynamic model are presented
The fish populations in the Baltic Sea have many problems, which are mainly caused by human influence
A responsible management must reduce the fishing effort to an environmentally acceptable level and call for the cooperation among the participating countries. This is of utmost importance, since the economic value of the catches depends on the stock and the biodiversity of the Baltic Sea
Summary
The fish populations in the Baltic Sea have many problems, which are mainly caused by human influence. A responsible management must reduce the fishing effort to an environmentally acceptable level and call for the cooperation among the participating countries. This is of utmost importance, since the economic value of the catches depends on the stock and the biodiversity of the Baltic Sea. Several interacting species are modeled, which inhabit in a common habitat with limited resources. A dynamic system is to be studied, which depends on several states and controls (e.g. the number of fishing boats). In many applications a cost functional is to be optimized, this is usually a functional of the state trajectory and the controls of the system. Numerical methods are obtained from the optimality conditions in order to calculate (approximately) optimal controls
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