Necessary optimality conditions for switched systems

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• 作者：A. S. Bortakovskii
• 刊名：Journal of Computer and Systems Sciences International
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：55
• 期：5
• 页码：712-724
• 全文大小：228 KB
• 刊物类别：Engineering
• 刊物主题：Control Engineering
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6530
• 卷排序：55

文摘

A dynamic system that models the operation of a switching device (switch) is considered. During the operation, the system changes its state a finite number of times. The change of state (switching) is described by a recurrent inclusion, which corresponds to the representation of the switch by a dynamic finite state machine with memory; instantaneous multiple switchings are admitted. The instants of time at which switchings are made and the number of switchings are not given in advance. They are found by optimizing a functional in which the number of switchings and the cost of each of them are taken into account. Necessary optimality conditions for such systems are proved. Different versions of the optimality conditions for different types of constraints are given. In particular, under additional convexity conditions, conditions that are similar to the maximum principle for discrete systems are obtained. The application of the optimality conditions is illustrated by examples.