The turnpike property in maximization of microbial metabolite production

We consider the problem of maximization of metabolite production in bacterial cells. Numerical methods showed that the major phase of the solutions for different initial states and final times is the singular regime which exhibits a special structure reminiscent of the turnpike phenomenon. We prove that singular trajectories indeed have the turnpike property by providing an estimate both on singular trajectories and on the associated controls. This result can be further used for construction of simple realistic suboptimal control strategies.