Optimal switching control of 1,3-propanediol fed-batch production with a cost on smooth feeding rate variation

• Published in: Nonlinear analysis. Hybrid systems Vol. 49; p. 101372
• Main Authors: Liu, Chongyang, Zhao, Qiaona
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2023
• Subjects: Fed-batch process; Nonlinear switched system; Optimal control; Parallel PSO; Total variation; Total variation; Fed-batch process; Parallel PSO; Nonlinear switched system; Optimal control
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2023.101372

In this paper, we propose a nonlinear switched control system for microbial 1,3-propanediol (1,3-PD) fed-batch production, where the smooth feeding rate of glycerol as well as the switching instants between batch process and feeding process are taken as control variables. To maximize 1,3-PD yield and minimize the fluctuation of feeding rate, we then present an optimal switching control problem with a cost on the smooth feeding rate variation and subject to path constraints reflecting the operational requirements. For solving this problem, we convert it to a series of parameter optimization problems by using a novel control parameterization scheme, a time-scaling transformation and a constraint transcription technique. An analytical expression of the total variation for the smooth feeding rate is also derived. On this basis, we develop a parallel Particle Swarm Optimization (PSO) algorithm together with the gradient-based optimization to solve the resulting problem. Finally, numerical simulations indicate that sacrificing a small amount of 1,3-PD can reduce the feeding rate variation significantly.