Robust Optimal Control of a Microbial Batch Culture Process

Abstract

This paper considers the microbial batch culture process for producing 1,3-propanediol (1,3-PD) via glycerol fermentation. Our goal was to design an optimal control scheme for this process, with the aim of balancing two (perhaps competing) objectives: (i) the process should yield a sufficiently high concentration of 1,3-PD at the terminal time and (ii) the process should be robust with respect to changes in various uncertain system parameters. Accordingly, we pose an optimal control problem, in which both process yield and process sensitivity are considered in the objective function. The control variables in this problem are the terminal time of the batch culture process and the initial concentrations of biomass and glycerol in the batch reactor. By performing a time-scaling transformation and introducing an auxiliary dynamic system to calculate process sensitivity, we obtain an equivalent optimal control problem Communicated by Mimmo Iannelli. 123J Optim Theory Appl in standard form. We then develop a particle swarm optimization algorithm for solving this equivalent problem. Finally, we explore the trade-off between process efficiency and process robustness via numerical simulations.

Experimental design suboptimization for the enzyme-catalytic nonlinear time-delay system in microbial batch culture

“…Here, on the basis of Eq. (10) and the method in [36,37], we obtain the result which is listed in Table 1.…”

“…However, that is often an invalid assumption, as parameters are subject to natural variability and uncertainties that are due to insufficient knowledge about the phenomenon under investigation. Similar to [36,37], we consider the system sensitivity with respect to the uncertain model parameters as follows:…”

“…As the authors demonstrated in [36,37], measures the rate at which the process yield changes in response to small changes in the model parameters. Therefore, we can calculate the values of to analyse the optimal control obtained by solving the problem (OCM).…”

“…After numerous experiments [37], it was clear that the convergence of NM method is the best when = 1, ˛ = 2, and ˇ = 0.5. That is, from a statistic standpoint, generally, the attachment direction u +1 = u c − u K is the feasible descent direction of objective function J(u).…”

Strong Stability of a Nonlinear Multi-Stage Dynamic System in Batch Culture of Glycerol Bioconversion to 1,3-Propanediol

“…A comparison of batch culture with continuous and fed-batch cultures has recently been come into investigators notice throughout the world as it can obtain the highest production concentration and molar yield 1,3-PD to glycerol [1]. Not only the nonlinear dynamic behaviour of microorganisms has been the objective of a number of theoretical works, but also much modelling research on the process of batch culture has been reported recently in [2,16,23,28]. However, for all the papers mentioned above, the strong stability is not taken into consideration in batch culture.…”