Author(s)

Dmitriy Stukalin, Werner H. Schmidt

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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.

Optimal Control Problems, Maximum Principle, Piecewise Constant Optimal Control, Bellman Principle

D. Stukalin and W. Schmidt, "Some Applications of Optimal Control in Sustainable Fishing in the Baltic Sea," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 854-865. doi: 10.4236/am.2011.27115.