Robust Optimal Control Of A Nonlinear Dynamical System In Batch Culture Process

This dissertation investigates the optimal control problem with the uncertain param-eters in batch culture process, which is one of the main fermentation types of glycerol bio conversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae. This work not on-ly shows the significance of the optimal control theory, but also provides a theoretical guidance for improving the yield of the final product 1,3-PD and mass production. This research is supported by the National Natural Science Foundation and the Fundamental Research Funds for the Central Universities. The main content and results obtained in this dissertation can be summarized as follows:1. In this dissertation, our goal is 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 the control variables are the terminal time of the batch culture process and the initial concentrations of biomass and glycerol in the batch reactor. We regarded process yield and process sensitivity as performance index, and established the nonlinear optimal control model. In addition, we developed a particle swarm optimization algorithm for solving this equivalent problem. Finally, we explored the trade-off between process efficiency and process robustness via numerical simulations.2. In the process of solving the above nonlinear optimal control problem, we encoun-tered two problems:(i) the terminal time is free instead of fixed; and (ii) the objective function contains a non-standard sensitivity term. To circumvent the first difficulty, we performed a time-scaling transformation technology. And then, by introducing an auxil-iary dynamic system to calculate process sensitivity, we obtained an equivalent optimal control problem in standard form.3. Since the optimal control problem is nonlinear and non-differentiable, we can not obtain the analytical solutions. In addition, many optimization algorithms which depend on gradient computation can only find the local optimal solution. In order to break through the limit, we developed a modified particle swarm optimization algorithm for solving this problem, and got the global optimal solutions of the problem. The numerical results show that the method is successful at the producing robust control strategies that achieve good performance while ensuring that sensitivity with respect to parameter changes is below acceptable levels.