Riemann-Liouville型分数阶导数的非线性估计(英文)

Nonlinear estimation of Riemann-Liouville type fractional-order derivative

中文关键词  分数阶微积分  Riemann-Liouville  非线性系统  自适应滑模  Gaussian白噪声

英文关键词  fractional calculus  Riemann-Liouville  nonlinear system  adaptive sliding mode  white Gaussian noise

中文摘要

      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.

英文摘要

      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.