{"title":"On the Optimal Control Function Diagrams in the Problem of the Movement of a Platform with Oscillators","authors":"O. R. Kayumov","doi":"10.1134/s1064230724700199","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider the problem of the time-optimal movement of a rigid body moving translationally along a horizontal straight line and carrying <i>n</i> linear oscillators. The only control force is applied to the platform and is limited in magnitude, and there is no friction. The system is transferred from a state of rest to a specified distance with vibration damping. The evolution of optimal control functions depending on the distance of the movement is investigated. A general approach to construct a visual diagram reflecting this evolution is proposed. To do this, a geometric interpretation of the necessary optimality conditions is used as properties of an auxiliary control curve in <i>n</i>-dimensional space. Numerical examples of constructing diagrams of the optimal control functions for a platform with three oscillators are given.</p>","PeriodicalId":50223,"journal":{"name":"Journal of Computer and Systems Sciences International","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and Systems Sciences International","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064230724700199","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the problem of the time-optimal movement of a rigid body moving translationally along a horizontal straight line and carrying n linear oscillators. The only control force is applied to the platform and is limited in magnitude, and there is no friction. The system is transferred from a state of rest to a specified distance with vibration damping. The evolution of optimal control functions depending on the distance of the movement is investigated. A general approach to construct a visual diagram reflecting this evolution is proposed. To do this, a geometric interpretation of the necessary optimality conditions is used as properties of an auxiliary control curve in n-dimensional space. Numerical examples of constructing diagrams of the optimal control functions for a platform with three oscillators are given.
摘要 我们考虑的问题是一个沿水平直线平移并携带 n 个线性振荡器的刚体的时间最优运动问题。唯一的控制力施加在平台上，且大小有限，没有摩擦力。系统从静止状态转移到指定距离时，会产生振动阻尼。研究了最佳控制函数随运动距离的变化情况。我们提出了一种构建可视化图表以反映这种演变的一般方法。为此，对必要最优条件的几何解释被用作 n 维空间中辅助控制曲线的属性。文中给出了构建具有三个振荡器的平台的最优控制函数图的数值示例。
期刊介绍：
Journal of Computer and System Sciences International is a journal published in collaboration with the Russian Academy of Sciences. It covers all areas of control theory and systems. The journal features papers on the theory and methods of control, as well as papers devoted to the study, design, modeling, development, and application of new control systems. The journal publishes papers that reflect contemporary research and development in the field of control. Particular attention is given to applications of computer methods and technologies to control theory and control engineering. The journal publishes proceedings of international scientific conferences in the form of collections of regular journal articles and reviews by top experts on topical problems of modern studies in control theory.
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