Bi-objective Optimal Control of Enzymatic Nonlinear Dynamical System for 1,3-Propanediol Transmembrane Transport in Microbial Batch Culture

This paper investigates the bi-objective dynamic optimization problem of a complex non-linear time-delay system during the glycerol metabolism process. In the biotransformation system, various mechanisms are considered, including enzymatic-catalytic kinetics and the regulation of the dha regulon. Hence, this paper develops a nonlinear time-delay dynamic system incorporating enzyme-catalytic and genetic regulation to describe the batch culture process of microorganisms, taking the productivity of 1,3-Propanediol(1,3-PD) and the consumption rate of glycerol as dual optimization objectives. The initial concentrations of biomass and glycerol, along with the terminal time of the process, are regarded as control variables. Through time-scale transformation, the problem is converted into an equivalent optimal control problem with a fixed terminal time. Subsequently, a constrained transcription technique along with a modified multi-objective particle swarm optimization algorithm (MOPSO) is invoked to solve the equivalent problem. The final numerical results demonstrate that, when the productivity of 1,3-PD is identical at the terminal time, the glycerol consumption rate has decreased by 27.79% compared to the previous value.