Parameter Identification And Optimal Control Of Nonlinaer Dynamical System For A Class Of Microbial Continuous Fermentation

This dissertation studies the model of parameter identification and product optimizationbased on the biological robustness under the background of glycerol bioconversion to1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K.pneumoniae)’s dismutation. Someproperties of the solution are proved. A parallel optimization algorithm based on parallelprinciple is constructed. Numerical results which are obtained from the algorithm provide anew foundation and reference for the experimental research of1,3-PD. The mainachievements are summarized as follows:1. Taking the flow rate and the feeding glycerol concentration as two constant valueoptimization variables, an optimization model of product1,3-PD is proposed. In considerationof the fact that some parameters of the system may be varied with the flow rate and thefeeding glycerol, a definition of robustness index which could reflect the change of everysubstance’s concentration is given for the nonlinear dynamic systems with unknownparameters on the basis of qualitative description of the biological robustness. To maximizethe products, a parameter selection model is presented by taking the concentration of1,3-PDat the steady time as cost functional, and the robustness index and the steady-state of systemare taken as constraints. According to the properties of the system, the existence of theoptimal solution to this model is demonstrated. A parallel particle swarm optimization-parameter selection algorithm (PPSO-OPSA) is established for seeking the optimal flow rateand the flow concentration of glycerol. Numerical results show that the product concentrationat the steady time under the optimal strategy has increased significantly. Meanwhile, thesystem with optimal parameters has a good robustness.2. The optimization problem with regard to the product1,3-PD is further discussed underthe circumstances that the flow rate and the concentration of glycerol that fed into the petridish are time varied. On the basis of the above work, a new robustness index is puttingforward. To maximize the concentration of1,3-PD at the steady time, the optimal controlmodel is constructed with taking the robustness index and the steady-state of system asconstraints. We investigate some properties of this model and its solution. A numerical algorithm for solving the problem is constructed based on a control method to parameterize.Numerical results verify the feasibility of this method. This approach provides a new patternand optimization strategy for later experimental study.