Turnpike property in optimal microbial metabolite production

Jean-Baptiste Caillau (1, 2, 3) , Walid Djema (4) , Jean-Luc Gouzé (4) , Sofya Maslovskaya (5) , Jean-Baptiste Pomet (2)

1 UniCA - Université Côte d'Azur
2 McTAO - Mathematics for Control, Transport and Applications
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 BIOCORE - Biological control of artificial ecosystems
5 UPB - Universität Paderborn

We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). By Pontryagin's maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic sub-optimal control strategies.

Mots clés: turnpike property; Fuller phenomenon; biological systems

Domaines: Optimisation et contrôle [math.OC]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Jean-Baptiste Caillau, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, Jean-Baptiste Pomet. Turnpike property in optimal microbial metabolite production. Journal of Optimization Theory and Applications, 2022, ⟨10.1007/s10957-022-02023-0⟩. ⟨hal-03328686v2⟩