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论文类型：期刊论文
发表时间：2011-01-01
发表刊物：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
收录刊物：SCIE
卷号：88
期号：2
页面范围：396-407
ISSN号：0020-7160
关键字：optimal control; switched autonomous system; switching instant; smoothing technique; fed-batch culture
摘要：A switched autonomous system is proposed to formulate the fed-batch culture process by taking the switching instants between the feed and batch processes as control variables. To maximize the concentration of 1,3-propanediol (1,3-PD) at the terminal time, an optimal control model subject to our proposed switched autonomous system and continuous state inequality constraints is then presented. A computational approach is developed to find the optimal switching instants in two aspects. On the one hand, the constraint transcription and smoothing techniques are applied to dealing with the continuous state inequality constraints; on the other hand, the first and the second derivatives of the cost functional, where the transformed state constraints are treated as a penalty function, are derived by the calculus of variations. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD at the terminal time can be increased considerably.