Bias-free Parameter Identification for Non-Commensurable Fractional Systems
Bias-free Parameter Identification for Non-Commensurable Fractional Systems
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DOI：
10.23919/ecc51009.2020.9143681
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Oliver Stark;M. Pfeifer;Stefan Krebs;S. Hohmann
中科院分区：
文献类型：
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作者：
Oliver Stark;M. Pfeifer;Stefan Krebs;S. Hohmann
本文研究了输出信号具有噪声观测的非离散分数阶系统的参数辨识问题。分数系统越来越多地用于描述复杂系统或记忆效应。如果系统不是静止的，实际的辨识方法不能处理输出信号的噪声观测。本文提出了一种调制函数法和辅助变量法相结合的方法。工具变量方法产生无偏估计，而不知道任何关于破坏输出信号的噪声。为了计算辅助变量，还利用短记忆原理扩展了计算分数系封闭解的算法。所提出的方法进行了比较，共同的最小二乘法通过数值模拟。
This paper deals with the parameter identification for non-commensurable fractional systems under noisy observations of the output signal. Fractional systems are increasingly used to describe complex systems or memory effects. Actual identification methods can not handle noisy observations of the output signal if the system is not at rest. In this paper, an approach is proposed which uses a combination of the modulating function method and the instrumental variable method. The instrumental variable method yields unbiased estimates without knowing anything about the noise which corrupts the output signal. To calculate the instrumental variables, an algorithm to calculate the closed-form solution of a fractional system is also extended by the short-memory principle. The presented approach is compared to the common least-squares method by a numerical simulation.