Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions

V. A. Srochko, V. G. Antonik
{"title":"Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions","authors":"V. A. Srochko, V. G. Antonik","doi":"10.26516/1997-7670.2023.45.24","DOIUrl":null,"url":null,"abstract":"Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.","PeriodicalId":42592,"journal":{"name":"Bulletin of Irkutsk State University-Series Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Irkutsk State University-Series Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26516/1997-7670.2023.45.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
具有外部作用的离散-连续形式线性二次问题的求解
研究了分段常数控制集上的两个线性二次问题。第一个问题包含被控系统右侧的离散扰动和带有符号不定矩阵的二次泛函中的不确定参数。它的解由保证结果规则得到,并以有限维极大极小问题的形式实现。得到了将目标函数转化为凹凸结构的参数的条件,并给出了有效求解该问题的可能性。这些是包含对称矩阵的极端特征值的线性不等式。第二个问题与离散变量中的泛函有关,它被定义为相位轨迹与外部影响的连续时间实现的偏差。它提供了在时间间隔的每个节点点上逐步搜索极值的机会。局部问题可以在有限次迭代中有效求解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.40
自引率
28.60%
发文量
19
审稿时长
8 weeks
期刊最新文献
Modernization of the educational potential under the conditions of partial military mobilization in Russia Modern research problems of modern sociology Retrospective analysis and prospects for further development of NATO operational thinking Russia-Germany energy cooperation: How paradigm change affects Germany’s economy and politics Political interest of the Russian state in participation in educational reforms: The problem of unspokenness
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1