一类非线性切换系统最优控制及在生物发酵中的应用

发布时间：2018-05-25 07:09

本文选题：切换系统 + 最优控制　；参考：《鲁东大学》2015年硕士论文

【摘要】：微生物批式流加发酵生产1,3-丙二醇(1,3-PD)具有天然的切换特性,为了提高其产量,目前已有研究者建立了微生物批式流加发酵生产1,3-PD的动力模型,但在最优控制求解方面,其算法受到了需要事先给定切换次数或切换序列的限制.针对新近出现的一类求解算法,本文对该算法的收敛性进行了研究,并将该算法应用到批式流加发酵切换最优控制问题中,验证了算法的有效性. 主要结果如下： 1.本文在一类非线性切换系统最优控制算法的基础上,通过分析数值最优解、理论最优解及其分片常值函数之间的关系,证明了当时间区间无限细分时,算法得到的切换最优控制数值解收敛于理论最优解,从而在理论上证明了算法是有效的.为算法的实际应用打下基础. 2.本文将上述算法应用到批式流加发酵生产1,3-PD的模型当中,在不需要事先给定切换次数或切换序列的前提下,借助控制参数化方法独立求解子系统的最优控制,并计算各子系统相应时刻的汉密尔顿函数值,进而获得相应时刻的切换规则,最终求得切换问题的最优控制.避免了以往寻找和优化切换控制的复杂过程.
[Abstract]:In order to increase its yield, some researchers have established a dynamic model for the production of 1o 3-PD by batch fermentation. However, in the aspect of optimal control solution, some researchers have established a dynamic model for the production of 1C 3-PD by batch fermentation, but in the aspect of optimal control solution, some researchers have established a dynamic model for the production of 1G 3-PD by batch fermentation. The algorithm is constrained by the need to predetermine the number or sequence of handovers. In this paper, the convergence of the new algorithm is studied, and the algorithm is applied to the optimal control problem of batch flow plus fermenting switching. The validity of the algorithm is verified. The main results are as follows: 1. On the basis of the optimal control algorithm for a class of nonlinear switched systems, by analyzing the relationship between the numerical optimal solution, the theoretical optimal solution and the piecewise constant function, it is proved that when the time interval is infinitely subdivided, The numerical solution of switching optimal control obtained by the algorithm converges to the theoretical optimal solution, which proves that the algorithm is effective in theory. It lays the foundation for the practical application of the algorithm. 2. In this paper, the algorithm is applied to the model of batch Flow-fermenting production of 1ka-3-PD, and the optimal control of the subsystem is solved independently by using the control parameterization method without the need to give the number or sequence of switching beforehand. The Hamilton function value of each subsystem at the corresponding time is calculated, and the switching rules at the corresponding time are obtained. Finally, the optimal control of the switching problem is obtained. The complex process of searching and optimizing switching control is avoided.
【学位授予单位】：鲁东大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O232

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