Optimal Control Of Nonlinear Switched Systems In Microbial Fed-batch Fermentation

This dissertation studies nonlinear switched dynamical systems and their optimal control problems in decoupled microbial fed-batch fermentation of glycerol bioconversion to 1,3-propanediol(1,3-PD). This research can not only develop the optimal control theory and optimization algorithm, but also provide certain reference for the practical applications. The main achievements are summarized follows:1. For the microbial fermentation process of glycerol to 1,3-propanediol(1,3-PD), a nonlinear switched dynamical system is studied in a decoupled microbial fed-batch ferme `ntation by considering comprehensively the evolution of concentration of the intracellular and extracellular substances. Taking the feeding rates of glycerol and alkali as decision variables, a switching optimal control model is formulated with the productivity of 1,3-PD as the performance index. A particle swarm optimization algorithm is established for seeking the optimal feeding rates of glycerol and alkali. Numerical results show that, by employing the optimal control policy, the concentration of 1,3-PD at the terminal time can be increased considerably.2. A novel switched system is established which is represented by a ten-dimensional nonlinear dynamical equation containing both extracellular and intracellular environments. Taking the feeding rates of glycerol and alkali, the switched times of glycerol and the mode sequence as the control variables, an optimal control model is proposed with the concentration of the terminal time 1,3-PD as performance index. In order to maximize the yield of 1,3-PD, the control parametrization technique and the exact penalty function method are used to solve the considered problem. Numerical results show that under the obtained optimal feeding rates of glycerol and alkali, switched times of glycerol and mode sequence, the productivity of 1,3-PD at the terminal time is increased significantly compared with previous results.3. A state-dependent switched system with mixed constraints is presented based on the uncoupled microbial fed-batch fermentation, in which both the number of mode switches and the mode sequence are unfixed. To maximize the yields of target product 1,3-PD, we formulate an optimal control problem with the concentration of 1,3-PD at the terminal time as performance index. An embedded optimal control problem is developed by introducing convex combinations of the modes and the constraints. We discuss the relationships between the switched optimal control problem and the corresponding embedded optimal control problem. In view of the parallel principle, a parallel algorithm is proposed for obtaining an optimal numerical solution of the considered problem. The numerical results show that the proposed algorithm is effective and provide a reference for practical fermentation experiments.