Geometric Optimal Control of the Generalized Lotka--Volterra Model of
the Intestinal Microbiome
We introduce the theoretical framework from geometric optimal control
for a control system modeled by the Generalized Lotka-Volterra (GLV)
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.