{"title":"Resolvents of the Ito Differential Equations Multiplicative with Respect to the State Vector","authors":"M. E. Shaikin","doi":"10.1134/s0005117923080088","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Integral representations of solutions of linear multiplicatively perturbed differential equations are obtained, the diffusion part of which is bilinear on the state vector and the vector of independent Wiener processes. Equations of such class serve as models of stochastic systems with control functioning under conditions of parametric uncertainty or undesirable influence of external disturbances. The concepts and analytical apparatus of the theory of Lie algebras are used to find integral representations and fundamental matrices of the equations.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-12-18","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://doi.org/10.1134/s0005117923080088","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
Integral representations of solutions of linear multiplicatively perturbed differential equations are obtained, the diffusion part of which is bilinear on the state vector and the vector of independent Wiener processes. Equations of such class serve as models of stochastic systems with control functioning under conditions of parametric uncertainty or undesirable influence of external disturbances. The concepts and analytical apparatus of the theory of Lie algebras are used to find integral representations and fundamental matrices of the equations.
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.).
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
