Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture

摘要

In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), theaim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yieldintensity of 1,3-PD as the performance index and the initial concentrationof biomass, glycerol, and terminal time as the control vector, we propose anoptimal control model subject to a multistage nonlinear dynamical system andconstraints of continuous state. A computational approach is constructed toseek the solution of the above model. Firstly, we transform the optimal controlproblem into the one with fixed terminal time. Secondly, we transcribe theoptimal control model into an unconstrained one based on the penalty functionsand an extension of the state space. Finally, by approximating the controlfunction with simple functions, we transform the unconstrained optimal controlproblem into a sequence of nonlinear programming problems, which can besolved using gradient-based optimization techniques. The convergence analysisand optimality function of the algorithm are also investigated. Numerical resultsshow that, by employing the optimal control, the concentration of 1,3-PD atthe terminal time can be increased, compared with the previous results.