{"title":"具有 Mittag-Leffler 稳定性的分数差分航天器模型的鲁棒性和动力学特征","authors":"Sobia Sultana","doi":"10.1515/phys-2024-0066","DOIUrl":null,"url":null,"abstract":"Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability\",\"authors\":\"Sobia Sultana\",\"doi\":\"10.1515/phys-2024-0066\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1515/phys-2024-0066\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1515/phys-2024-0066","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.