{"title":"具有不确定输入时延的系统的鲁棒 H∞ 稳定性","authors":"","doi":"10.1016/j.jfranklin.2024.107223","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> stabilization approach for actively controlled systems that include uncertain input time-delay. The approach comprises two essential steps: (1) converting a controlled system with uncertain time-delay to have only deterministic time-delay through a time-scale transformation; and (2) applying the Chebyshev spectral continuous time approximation (CHsCTA) method and defining appropriate extension matrices to transform the system so there are no time-delays. A robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> control design is implemented on the transformed system, which facilitates the derivation of a robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> controller. An iterative algorithm is proposed for computing the feedback gain matrix, which overcomes the challenges posed by the nonlinear coupling terms when solving the matrix inequalities. Case studies validate the effectiveness of the proposed control algorithm, which, through comparison with existing control algorithms, is shown to be less conservative.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0016003224006446/pdfft?md5=4f39ac153d46253bd0ebf74e361c9c0a&pid=1-s2.0-S0016003224006446-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Robust H∞ stabilization for systems with uncertain input time-delay\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107223\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper presents a robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> stabilization approach for actively controlled systems that include uncertain input time-delay. The approach comprises two essential steps: (1) converting a controlled system with uncertain time-delay to have only deterministic time-delay through a time-scale transformation; and (2) applying the Chebyshev spectral continuous time approximation (CHsCTA) method and defining appropriate extension matrices to transform the system so there are no time-delays. A robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> control design is implemented on the transformed system, which facilitates the derivation of a robust <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> controller. An iterative algorithm is proposed for computing the feedback gain matrix, which overcomes the challenges posed by the nonlinear coupling terms when solving the matrix inequalities. Case studies validate the effectiveness of the proposed control algorithm, which, through comparison with existing control algorithms, is shown to be less conservative.</p></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0016003224006446/pdfft?md5=4f39ac153d46253bd0ebf74e361c9c0a&pid=1-s2.0-S0016003224006446-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0016003224006446\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224006446","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Robust H∞ stabilization for systems with uncertain input time-delay
This paper presents a robust stabilization approach for actively controlled systems that include uncertain input time-delay. The approach comprises two essential steps: (1) converting a controlled system with uncertain time-delay to have only deterministic time-delay through a time-scale transformation; and (2) applying the Chebyshev spectral continuous time approximation (CHsCTA) method and defining appropriate extension matrices to transform the system so there are no time-delays. A robust control design is implemented on the transformed system, which facilitates the derivation of a robust controller. An iterative algorithm is proposed for computing the feedback gain matrix, which overcomes the challenges posed by the nonlinear coupling terms when solving the matrix inequalities. Case studies validate the effectiveness of the proposed control algorithm, which, through comparison with existing control algorithms, is shown to be less conservative.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.