Observability of Time-Varying Fractional Dynamical Systems with Caputo Fractional Derivative

IF 1.1 3区 数学 Q1 MATHEMATICS
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引用次数: 0

Abstract

Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative properties of such a system in a fractional sense are hardly examined. Observability is one property where the system’s initial states are determined based on the output of some observation system. In this paper, we investigate the observability of time-varying fractional dynamical systems. A state-transition matrix represents the solution of the time-varying fractional dynamical systems. The observability results of linear and nonlinear systems are obtained using the Gramian matrix technique and the Banach contraction mapping theorem respectively. The obtained theoretical results for the observability of the time-varying fractional dynamical systems are compared with those of the time-invariant fractional dynamical system (FDS). Several numerical examples are provided to validate the theoretical results. Also, a numerical example to study the observability of a fractional spring–mass system is provided to verify the applicability of this study.

具有卡普托分式衍生物的时变分式动态系统的可观测性
摘要 利用具有随时间变化的扰动的真实数据建立动态系统模型,可以更好地利用时变系统。这种系统在分数意义上的定性属性几乎没有得到研究。可观测性就是根据某个观测系统的输出确定系统初始状态的一种特性。本文将研究时变分数动力系统的可观测性。状态转换矩阵表示时变分数动力系统的解。利用格拉米矩阵技术和巴拿赫收缩映射定理分别获得了线性系统和非线性系统的可观测性结果。所获得的时变分数动力系统可观测性理论结果与时不变分数动力系统(FDS)的可观测性结果进行了比较。还提供了几个数值示例来验证理论结果。此外,还提供了一个研究分数弹簧-质量系统可观测性的数值示例,以验证本研究的适用性。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
261
审稿时长
6-12 weeks
期刊介绍: The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.
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