Polynomial profits in renewable resources management. (October 2017)

• Record Type: Journal Article
• Authors: Colombo, Rinaldo M.; Garavello, Mauro
• Is Part Of: Nonlinear analysis. Volume 37(2017)
• Page Start: 374
• Page End: 386
• Publication Date: 2017-10
• Subjects: Management of biological resources -- Optimal control of conservation laws -- Renewal equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.03.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.