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

Hamza Ben Brahim, F. E. El Alaoui, Khalid Zguaid
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引用次数: 0

摘要

本研究的目的是为一类微分阶数介于 1 和 2 之间的黎曼-刘维尔型线性时分数系统提出可观测性概念。为了实现这一目标,我们首先定义了可观测性的概念及其特征,然后扩展了希尔伯特唯一性方法(HUM)以确定系统的初始状态。该方法将重构问题转化为可解性问题,从而产生了一种计算初始状态的算法。最后一节将通过数值模拟演示所提算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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