{"title":"关于时间分数系统的可观测性和初始状态重构的一些结果","authors":"Hamza Ben Brahim, F. E. El Alaoui, Khalid Zguaid","doi":"10.11121/ijocta.1468","DOIUrl":null,"url":null,"abstract":"The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the Hilbert Uniqueness Method (HUM) to determine the system's initial state. This method converts the reconstruction problem into a solvability one, leading to an algorithm that calculates the initial state. The effectiveness of the proposed algorithm is demonstrated through numerical simulations, which are presented in the final section.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"104 s410","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some results regarding observability and initial state reconstruction for time-fractional systems\",\"authors\":\"Hamza Ben Brahim, F. E. El Alaoui, Khalid Zguaid\",\"doi\":\"10.11121/ijocta.1468\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the Hilbert Uniqueness Method (HUM) to determine the system's initial state. This method converts the reconstruction problem into a solvability one, leading to an algorithm that calculates the initial state. The effectiveness of the proposed algorithm is demonstrated through numerical simulations, which are presented in the final section.\",\"PeriodicalId\":505378,\"journal\":{\"name\":\"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)\",\"volume\":\"104 s410\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11121/ijocta.1468\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11121/ijocta.1468","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some results regarding observability and initial state reconstruction for time-fractional systems
The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the Hilbert Uniqueness Method (HUM) to determine the system's initial state. This method converts the reconstruction problem into a solvability one, leading to an algorithm that calculates the initial state. The effectiveness of the proposed algorithm is demonstrated through numerical simulations, which are presented in the final section.