Geometric optimal control of the generalized Lotka–Volterra model of the intestinal microbiome

Abstract

We introduce the theoretical framework from geometric optimal control for a control system modeled by the generalized Lotka–Volterra equation, motivated by restoring the gut microbiota infected by Clostridium difficile combining antibiotic treatment and fecal injection. We consider both permanent control and sampled‐data control related to the medical protocols.