{"title":"Necessary Extremum Conditions and the Neustadt–Eaton Method in the Time-Optimal Control Problem for a Group of Nonsynchronous Oscillators","authors":"L. M. Berlin, A. A. Galyaev, P. V. Lysenko","doi":"10.1134/S0005117924060043","DOIUrl":null,"url":null,"abstract":"<p>The time-optimal control problem for an arbitrary number of nonsynchronous oscillators with a limited scalar control is considered. An analytical investigation of the problem is performed. The property of strong accessibility and global controllability is proved, and a program control is found that brings the system from the origin to a fixed point in the shortest time. Trajectories satisfying both the motion equations of the system and the additional conditions based on the matrix nondegeneracy conditions of the relay control have been found for bringing a group of oscillators to the origin. Two classification methods of trajectories according to the number of control switchings are compared: the one based on the necessary extremum conditions and the Neustadt–Eaton numerical algorithm.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automation and Remote Control","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1134/S0005117924060043","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The time-optimal control problem for an arbitrary number of nonsynchronous oscillators with a limited scalar control is considered. An analytical investigation of the problem is performed. The property of strong accessibility and global controllability is proved, and a program control is found that brings the system from the origin to a fixed point in the shortest time. Trajectories satisfying both the motion equations of the system and the additional conditions based on the matrix nondegeneracy conditions of the relay control have been found for bringing a group of oscillators to the origin. Two classification methods of trajectories according to the number of control switchings are compared: the one based on the necessary extremum conditions and the Neustadt–Eaton numerical algorithm.
期刊介绍：
Automation and Remote Control is one of the first journals on control theory. The scope of the journal is control theory problems and applications. The journal publishes reviews, original articles, and short communications (deterministic, stochastic, adaptive, and robust formulations) and its applications (computer control, components and instruments, process control, social and economy control, etc.).
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