Identification And Optimal Control Of Non-Smooth Dynamical Systems In The Processes Of Fed-Batch And Continuous Culture

This dissertation investigates the identification and optimal control of a class of nonlinear impulsive system and non-smooth nonlinear dynamical system in the process of bioconversion glycerol to1,3-propanediol. According to the characteristic of fed-batch culture, a nonlinear state-dependent impulsive system is established to formulate the process of the culture. In terms of the transports of substrate and product across cell membrane, and the effects of the interme-diate in the continuous culture process, we develop a non-smooth nonlinear eight-dimensional dynamical system to simulate and optimize the process. The main contributions of the disserta-tion are summarized as follows:1. Taking the feeding process as a state-dependent impulses process, a nonlinear state-dependent impulsive system is proposed to formulate the process of fed-batch culture. The existence, uniqueness and regularity of solution to the system and continuous depen-dence of the solution on initial value and parameters are proved. Regarding the absolute error between the experimental results and calculated values as the performance index, a parameter identification model is presented. The identifiability of the parameter identifi-cation model is also proved. Finally, an improved particle swarm optimization algorithm is constructed to find the optimal parameters for the model. Numerical results show that the nonlinear state-dependent impulsive system can be used to describe the fed-batch culture better.2. During the process of fed-batch culture, how much substrate to feed is important. In this dissertation, a nonlinear impulsive controlled system, in which the volume of feeding is the control variable and both jumps size of state and impulsive moments are state-dependent, is proposed to formulate the fed-batch fermentation process. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system and subject to the continuous state inequality constraint and the control constraint is presented. In order to deduce the optimality conditions, the optimal control model is transcribed into an equivalent one by treating the constraints. Finally, the optimality conditions of the optimal control model are investigated by calculus of variations.3. In this dissertation, an eight-dimensional non-smooth nonlinear dynamic system is devel-oped to formulate the continuous culture of bioconversion glycerol to1,3-PD, in which the passive diffusion and active transport of glycerol and1,3-PD across cell membrane, and3-hydroxypropionaldehyde inhibition to cells growth for its toxicity and to the ac-tivity of GDHt and PDOR when its concentration is higher than a certain value are all taken into consideration. Then, the existence, uniqueness, continuous dependence of the solution on the parameter vector and the compactness of solution set are all proved. Tak-ing the mean relative error between the experimental data and calculated values as the cost functional, a parameter identification model involving multiple eight-dimensional non-smooth nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. An improved parallel particle swarm optimization algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results show that the nonlinear dynamic model can describe the fermentation process better and the algorithm is effective to solve the parameter identification model.