{"title":"二维有界控制线性离散系统作用速度问题的超椭球逼近","authors":"D.N. Ibragimov, V.M. Podgornaya","doi":"10.17759/mda.2023130209","DOIUrl":null,"url":null,"abstract":"<p>The paper considers a two-dimensional linear discrete system with bounded control. For the system, the problem of speed is solved, that is, the construction of a control process that transfers the system from the initial state to the origin in the minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure. Examples are considered in the paper.</p>","PeriodicalId":498071,"journal":{"name":"Modelirovanie i analiz dannyh","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control\",\"authors\":\"D.N. Ibragimov, V.M. Podgornaya\",\"doi\":\"10.17759/mda.2023130209\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The paper considers a two-dimensional linear discrete system with bounded control. For the system, the problem of speed is solved, that is, the construction of a control process that transfers the system from the initial state to the origin in the minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure. Examples are considered in the paper.</p>\",\"PeriodicalId\":498071,\"journal\":{\"name\":\"Modelirovanie i analiz dannyh\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modelirovanie i analiz dannyh\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17759/mda.2023130209\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modelirovanie i analiz dannyh","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17759/mda.2023130209","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Superellipsoidal Approximations in the Speed-in-action Problem for a Two-dimensional Linear Discrete System with Bounded Control
The paper considers a two-dimensional linear discrete system with bounded control. For the system, the problem of speed is solved, that is, the construction of a control process that transfers the system from the initial state to the origin in the minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure. Examples are considered in the paper.
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