Riemann-Liouville型分数阶导数的非线性估计  

Nonlinear estimation ofRiemann-Liouville type fractional-order derivative

作　　者：郭玉祥 马保离[2] 张庆平 占生宝 GUO Yu-xiang;MA Bao-li;ZHANG Qing-ping;ZHAN Sheng-bao(School of Electronic Engineering and Intelligent Manufacturing,Anqing Normal University,Anqing Anhui 246011,China;School of Automation Science and Electrical Engineering,Beijing University of Aeronautics and Astronautics,Beijing 100191,China;School of Information Science and Technology,University of Science and Technology of China,Hefei Anhui 230026,China)

机构地区：[1]安庆师范大学电子工程与智能制造学院,安徽安庆246011 [2]北京航空航天大学自动化科学与电气工程学院,北京100191 [3]中国科学技术大学信息科学技术学院,安徽合肥230026

出　　处：《控制理论与应用》2023年第2期256-266,共11页Control Theory & Applications

基　　金：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);the National Natural Science Foundation of Anhui Province (gxbjZD2021063)。

摘　　要：本文主要研究任意有界连续信号的Riemann-Liouville分数阶导数估计问题.当分数阶α属于0到1时,首先利用滑模技术提出一种有界连续信号分数阶导数的非线性估计方法;然后将其结果推广至分数阶α∈R+的情况,并给出相应的非线性估计方案.借助Riemann-Liouville分数阶微积分频率分布模型,本文详细分析讨论了所给分数阶导数非线性估计的收敛性问题,并得到相应闭环系统是渐近稳定的结论.文中所提方法的主要优点是在事先未知给定信号分数阶导数上界的情况下,不仅能自适应地估计其Riemann-Liouville分数阶导数,而且当信号中含有随机噪声和不确定扰动时依然能正常工作.数值仿真实例验证了本文所给估计方法的可行性和有效性.This paper mainly concerns about the problem of estimation of the Riemann-Liouville fractional derivative ofarbitrarily bounded continuous signal. By using sliding mode technique, a nonlinear fractional-order derivative estimator ofa bounded continuous signal for the order α between 0 and 1 is proposed firstly. Then it is extended to the case of arbitraryorder α ∈ R+, and the corresponding estimation scheme is also established. The convergence of the presented estimatoris 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 cannot only adaptively estimate the Riemann-Liouville fractional derivative of a given signal that is not clear about the upperbound of fractional derivative itself in advance, but also adapt to the uncertain disturbances or stochastic noise environmentin system. Numerical simulation results of an example are used to verify the practicality and availability of our givenestimation 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 

分 类 号：O212.1[理学—概率论与数理统计]