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Polynomial profits in renewable resources management. (English) Zbl 1405.91490

Summary: A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the target cost function is polynomial in the control. In specific situations, further information about the form of this dependence is obtained. As a consequence, in some cases the optimal control is proved to be necessarily bang-bang, in other cases the computations necessary to find the optimal control are significantly reduced.

MSC:

91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
05C90 Applications of graph theory
49N90 Applications of optimal control and differential games
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