控制理论与应用2023，Vol.40Issue(2)：256-266,11.DOI:10.7641/CTA.2022.11295
Riemann-Liouville型分数阶导数的非线性估计
Nonlinear estimation of Riemann-Liouville type fractional-order derivative
摘要
Abstract
This paper mainly concerns about the problem of estimation of the Riemann-Liouville fractional derivative of arbitrarily bounded continuous signal.By using sliding mode technique,a nonlinear fractional-order derivative estimator of a bounded continuous signal for the order α between 0 and 1 is proposed firstly.Then it is extended to the case of arbitrary order α ∈ R+,and the corresponding estimation scheme is also established.The convergence of the presented estimator is discussed in more detail with the assistance of frequency distributed model of the Riemann-Liouville fractional calculus.Meanwhile the matching closed-loop plant is asymptotically stable.The major advantages of the proposed methodology can not only adaptively estimate the Riemann-Liouville fractional derivative of a given signal that is not clear about the upper bound of fractional derivative itself in advance,but also adapt to the uncertain disturbances or stochastic noise environment in system.Numerical simulation results of an example are used to verify the practicality and availability of our given estimation scheme.关键词
分数阶微积分/Riemann-Liouville/非线性系统/自适应滑模/Gaussian白噪声Key words
fractional calculus/Riemann-Liouville/nonlinear system/adaptive sliding mode/white Gaussian noise引用本文复制引用
郭玉祥,马保离,张庆平,占生宝..Riemann-Liouville型分数阶导数的非线性估计[J].控制理论与应用,2023,40(2):256-266,11.基金项目
Supported by the Key Project of Universities Natural Science Research of Anhui Province(KJ2021A0638,KJ2020A0509),the National Natural Science Foundation of China(61573034,61327807,11705003)and the National Natural Science Foundation of Anhui Province(gxbjZD2021063). （KJ2021A0638,KJ2020A0509）
