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  本文選題：切換系統(tǒng) + 最優(yōu)控制��； 參考：《魯東大學(xué)》2015年碩士論文

【摘要】：微生物批式流加發(fā)酵生產(chǎn)1,3-丙二醇(1,3-PD)具有天然的切換特性,為了提高其產(chǎn)量,目前已有研究者建立了微生物批式流加發(fā)酵生產(chǎn)1,3-PD的動力模型,但在最優(yōu)控制求解方面,其算法受到了需要事先給定切換次數(shù)或切換序列的限制.針對新近出現(xiàn)的一類求解算法,本文對該算法的收斂性進(jìn)行了研究,并將該算法應(yīng)用到批式流加發(fā)酵切換最優(yōu)控制問題中,驗(yàn)證了算法的有效性. 主要結(jié)果如下： 1.本文在一類非線性切換系統(tǒng)最優(yōu)控制算法的基礎(chǔ)上,通過分析數(shù)值最優(yōu)解、理論最優(yōu)解及其分片常值函數(shù)之間的關(guān)系,證明了當(dāng)時間區(qū)間無限細(xì)分時,算法得到的切換最優(yōu)控制數(shù)值解收斂于理論最優(yōu)解,從而在理論上證明了算法是有效的.為算法的實(shí)際應(yīng)用打下基礎(chǔ). 2.本文將上述算法應(yīng)用到批式流加發(fā)酵生產(chǎn)1,3-PD的模型當(dāng)中,在不需要事先給定切換次數(shù)或切換序列的前提下,借助控制參數(shù)化方法獨(dú)立求解子系統(tǒng)的最優(yōu)控制,并計(jì)算各子系統(tǒng)相應(yīng)時刻的漢密爾頓函數(shù)值,進(jìn)而獲得相應(yīng)時刻的切換規(guī)則,最終求得切換問題的最優(yōu)控制.避免了以往尋找和優(yōu)化切換控制的復(fù)雜過程.
[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.
【學(xué)位授予單位】：魯東大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O232

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本文編號：1932553