Optimal control of a coupled degenerate population dynamics model with unknown birth rates

  • Cyrille Kenne Laboratoire LAMIA, Universit\'e des Antilles,\\ Campus Fouillole, 97159 Pointe-{\`a}-Pitre Guadeloupe (FWI)-\\ University of Buea, Department of Mathematics, Buea, Cameroon
  • Pascal Zongo Laboratoire L3MA, UFR STE et IUT, Universit\'e\\ des Antilles, Schoelcher, Martinique
  • Ren'e Dorville Laboratoire L3MA, UFR STE et IUT, Universit\'e\\ des Antilles, Schoelcher, Martinique\
  • Gis`ele Mophou Laboratoire LAMIA, Universit\'e des Antilles,\\ Campus Fouillole, 97159 Pointe-{\`a}-Pitre Guadeloupe (FWI)

Abstract

We consider a coupled model of degenerate population dynamics with age dependence and spatial structure but with unknown data on the birth rate of individuals. Using the notion of low-regret, we prove that we can bring the state of the second population in a given region to a desired state by acting on the first population via a localized control over a part of habitat. We provide the optimality systems that characterize the adapted low-regret control and prove its convergence to a so-called no-regret control that we characterize.

Published
2021-11-23