{"title":"SMC for discrete singular stochastic jump systems under semi-Markov kernel","authors":"","doi":"10.1016/j.jfranklin.2024.107250","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, the sliding mode control (SMC) is investigated for discrete singular stochastic semi-Markov jump systems under a semi-Markov kernel. Based on the remarkable application background and advantages in modeling complex dynamic systems, singular semi-Markov jump systems are utilized to address discrete SMC issues. A mode-dependent sliding function with a singular matrix is considered to reduce the effects of the numerical problems. The main aim is to use an improved approach to eliminate the matrix power terms so that the underlying augmented system can realize mean-square admissibility. An appropriate SMC law is constructed to achieve the reachability of the quasi-sliding mode, overcoming the difficulty caused by parameter uncertainty. Finally, the effectiveness of the SMC approach is verified using a DC motor model.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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/S0016003224006719","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}
引用次数: 0
Abstract
In this study, the sliding mode control (SMC) is investigated for discrete singular stochastic semi-Markov jump systems under a semi-Markov kernel. Based on the remarkable application background and advantages in modeling complex dynamic systems, singular semi-Markov jump systems are utilized to address discrete SMC issues. A mode-dependent sliding function with a singular matrix is considered to reduce the effects of the numerical problems. The main aim is to use an improved approach to eliminate the matrix power terms so that the underlying augmented system can realize mean-square admissibility. An appropriate SMC law is constructed to achieve the reachability of the quasi-sliding mode, overcoming the difficulty caused by parameter uncertainty. Finally, the effectiveness of the SMC approach is verified using a DC motor model.
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.