{"title":"A matrix approach to the analysis and computation of robust cycles for Boolean control networks with disturbances","authors":"Lei Deng, Shihua Fu, Xinling Li, Jianjun Wang","doi":"10.1007/s12190-024-02158-5","DOIUrl":null,"url":null,"abstract":"<p>This paper studies several types of robust control cycles (RCCs) for the Boolean control networks (BCNs) affected by disturbances using semi-tensor product of matrices, and provides their computing methods. First, the cycles of a BCN are classified as strong RCCs and weak RCCs according to their ability to resist disturbances. Secondly, the properties of the states on a cycle for the BCNs are revealed, based on which all the RCCs whose weak connecting degree is not more than one with certain length are obtained. Moreover, the controls to ensure that the state trajectories form RCCs are designed. Finally, some examples are given to demonstrate the effectiveness of the obtained theoretical results, as well as to show the applications of these results.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"1 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02158-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies several types of robust control cycles (RCCs) for the Boolean control networks (BCNs) affected by disturbances using semi-tensor product of matrices, and provides their computing methods. First, the cycles of a BCN are classified as strong RCCs and weak RCCs according to their ability to resist disturbances. Secondly, the properties of the states on a cycle for the BCNs are revealed, based on which all the RCCs whose weak connecting degree is not more than one with certain length are obtained. Moreover, the controls to ensure that the state trajectories form RCCs are designed. Finally, some examples are given to demonstrate the effectiveness of the obtained theoretical results, as well as to show the applications of these results.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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