Turnpike Property in Optimal Microbial Metabolite Production

We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to 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 suboptimal control strategies.