Belgacem Tikialine, Hadj Ammar Tedjani, A. Kelleche
In this paper, we are interested to stabilize an axially moving string subject to external disturbances. We assume that the disturbance may increases exponentially. We employ the active disturbance rejection control (ADRC) approach to estimate the disturbance. We design a disturbance observer that has time-varying gain so that the disturbance can be estimated with an exponential way. In order to stabilize the closed loop system, we use a control constructed through a high-gain adaptive velocity feedback. The existence and uniqueness of solution of the closed loop system is dealt with in the framework of the nonlinear semigroup theory by using a theorem due to Crandall-Liggett. It is shown that the formulated control is capable of stabilizing exponentially the closed loop system. The obtained results are also valid for the immobile case ($v=0$) and the present work improves certain previous results.
{"title":"High-gain adaptive boundary stabilization for an axially moving string subject to unbounded boundary disturbance","authors":"Belgacem Tikialine, Hadj Ammar Tedjani, A. Kelleche","doi":"10.52846/ami.v48i1.1398","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1398","url":null,"abstract":"In this paper, we are interested to stabilize an axially moving string subject to external disturbances. We assume that the disturbance may increases exponentially. We employ the active disturbance rejection control (ADRC) approach to estimate the disturbance. We design a disturbance observer that has time-varying gain so that the disturbance can be estimated with an exponential way. In order to stabilize the closed loop system, we use a control constructed through a high-gain adaptive velocity feedback. The existence and uniqueness of solution of the closed loop system is dealt with in the framework of the nonlinear semigroup theory by using a theorem due to Crandall-Liggett. It is shown that the formulated control is capable of stabilizing exponentially the closed loop system. The obtained results are also valid for the immobile case ($v=0$) and the present work improves certain previous results.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81712971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
"Caputo fractional differential equations with impulses are a very useful apparatus for adequate modeling of the dynamics of many rea world problems. It requires developments of good and consistent theoretical proofs and the results for various problems. In this note we point out and correct the statement of the boundary value problem with Riemann--Liouville fractional integral for impulsive Caputo fractional differential equation studied in the paper "" A. Zada, B. Dayyan, Stability analysis for a class of implicit fractional differential equations with instantaneous impulses and Riemann--Liouville boundary conditions, Ann. Univ. Craiova, Math. Comput. Sci. Ser., 47 (2020), 88-110."""
“带脉冲的卡普托分数阶微分方程是一种非常有用的工具，可以充分模拟许多现实世界问题的动力学。它要求对各种问题发展出良好和一致的理论证明和结果。a . Zada, B. Dayyan，一类具有瞬时脉冲和Riemann- Liouville边界条件的隐式分数阶微分方程的稳定性分析，在本文中，我们指出并修正了论文中研究的脉冲Caputo分数阶微分方程的Riemann- Liouville分数积分边值问题的表述。克拉约瓦大学，数学专业。第一版。科学。爵士。， 47(2020)， 88-110。”＂＂
{"title":"Comments on the paper \"A. Zada, B. Dayyan, Stability analysis for a class of implicit fractional differential equations with instantaneous impulses and Riemann--Liouville boundary conditions, Ann. Univ. Craiova, Math. Comput. Sci. Ser., (2020), 88-110\"","authors":"S. Hristova, A. Zada","doi":"10.52846/ami.v48i1.1469","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1469","url":null,"abstract":"\"Caputo fractional differential equations with impulses are a very useful apparatus for adequate modeling of the dynamics of many rea world problems. It requires developments of good and consistent theoretical proofs and the results for various problems. In this note we point out and correct the statement of the boundary value problem with Riemann--Liouville fractional integral for impulsive Caputo fractional differential equation studied in the paper \"\" A. Zada, B. Dayyan, Stability analysis for a class of implicit fractional differential equations with instantaneous impulses and Riemann--Liouville boundary conditions, Ann. Univ. Craiova, Math. Comput. Sci. Ser., 47 (2020), 88-110.\"\"\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87156187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we adapt an algorithm from the multiple attribute decision making field in order to be used in pattern recognition, working with intuitionistic fuzzy sets and intuitionistic fuzzy multi sets. Our method is implemented in two versions: using the score matrix (that is characteristic of decision making problems) and using a similarity measure (that is characteristic of pattern recognition problems). Firstly, the method is built to work with intuitionistic fuzzy sets and after it is extended for intuitionistic fuzzy multi sets. Experimental results demonstrate the superiority of the second versions in pattern recognition problems. For each example we compare our results with those given by other measures whose accuracy has been validated by the respective examples and we conclude that our method can be successfully used in pattern recognition instead of some specific methods in this area.
{"title":"Pattern recognition based on multiple attribute decision making in intuitionistic fuzzy environment","authors":"I. Iancu","doi":"10.52846/ami.v48i1.1465","DOIUrl":"https://doi.org/10.52846/ami.v48i1.1465","url":null,"abstract":"In this paper we adapt an algorithm from the multiple attribute decision making field in order to be used in pattern recognition, working with intuitionistic fuzzy sets and intuitionistic fuzzy multi sets. Our method is implemented in two versions: using the score matrix (that is characteristic of decision making problems) and using a similarity measure (that is characteristic of pattern recognition problems). Firstly, the method is built to work with intuitionistic fuzzy sets and after it is extended for intuitionistic fuzzy multi sets. Experimental results demonstrate the superiority of the second versions in pattern recognition problems. For each example we compare our results with those given by other measures whose accuracy has been validated by the respective examples and we conclude that our method can be successfully used in pattern recognition instead of some specific methods in this area.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84201413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The concept of statistical convergence was presented by Fast [18]. This concept was extended to the double sequences by Mursaleen and Edely 23 . In this paper, we define statistical analogues of convergence and Cauchy for triple sequences on probabilistic normed space.
{"title":"Statistical Convergence of Triple Sequences on Probabilistic Normed Space","authors":"E. Savaş, A. Esi","doi":"10.14419/GJMA.V1I2.885","DOIUrl":"https://doi.org/10.14419/GJMA.V1I2.885","url":null,"abstract":"The concept of statistical convergence was presented by Fast [18]. This concept was extended to the double sequences by Mursaleen and Edely 23 . In this paper, we define statistical analogues of convergence and Cauchy for triple sequences on probabilistic normed space.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2012-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78747386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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