Optimal Control of the Lotka-Volterra Equations with Applications

Bernard Bonnard (1, 2) , Jérémy Rouot (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 McTAO - Mathematics for Control, Transport and Applications
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

In this article, the Lotka-Volterra model is analyzed to reduce the infection of a complex microbiote. The problem is set as an optimal control problem, where controls are associated to antibiotic or probiotic agents, or transplantations and bactericides. Candidates as minimizers are selected using the Maximum Principle and the closed loop optimal solution is discussed. In particular a 2d-model is constructed with 4 parameters to compute the optimal synthesis using homotopies on the parameters.

Mots clés: Maximum Principle; Regular synthesis; Population dynamics; Lotka-Volterra equations; Optimal control

Domaines: Optimisation et contrôle [math.OC]

Bernard Bonnard, Jérémy Rouot. Optimal Control of the Lotka-Volterra Equations with Applications. 2022. ⟨hal-03829465v1⟩