Robust bi-objective optimal control of 1,3-propanediol microbial batch production process

Abstract

This paper considers optimal control of glycerol producing 1,3-propanediol (1,3-PD) in batch process with uncertain time-delay and kinetic parameters. Based on a dynamic system with uncertain time-delay and kinetic parameters describing the batch process, we propose a robust bi-objective optimal control model, in which 1,3-PD productivity and glycerol consumption rate, and their semi-relative sensitivities with respect to the uncertain parameters are all involved in the vector objective. The control variables in this problem are the initial concentrations of biomass and glycerol and the terminal time of the process. Then, by introducing auxiliary time-delay systems and performing a time-scaling transformation, we transform the robust bi-objective optimal control problem into an equivalent bi-objective optimal control problem in standard form. Furthermore, we convert the equivalent optimal control problem into a sequence of solvable single-objective optimal control problems by using the normalized normal constraint method together with the constraint transcription technique. To solve each of the resulting optimal control problems, we develop a novel gradient-based solution method. Finally, numerical results are provided to verify the effectiveness of the proposed solution approach.