Optimal control of microbial production in the chemostat

In this work, we study the problem of maximizing microbial production within a continuous stirred-tank reactor with n ≥ 1 species and one substrate. The interaction between is described by chemostat system including mutation factor. optimization falls into an optimal control Lagrange type in which parameter dilution rate reactor. Thanks to Pontryagin Maximum Principle, obtain necessary conditions on controls that involve singular arc. These computations are highlighted thanks numerical simulations via direct method. We also related at steady-state provides insight solutions terms turnpike phenomenon.