Meng Lihong, Yang Xu, Zulfiqar Umair, Du Xin
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China.
Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education (Northeast Electric Power University), Jilin 132012, China.
Math Biosci Eng. 2021 Jan 8;18(2):1063-1076. doi: 10.3934/mbe.2021058.
In this paper we propose a data driven realization and model order reduction (MOR) for linear fractional-order system (FoS) by applying the Loewner-matrix method. Given the interpolation data which obtained by sampling the transfer function of a FoS, the minimal fractional-order state space descriptor model that matching the interpolation data is constructed with low computational cost. Based on the framework, the commensurate order α of the fractional-order system is estimated by solving a least squares optimization in terms of sample data in case of unknown order-α. In addition, we present an integer-order approximation model using the interpolation method in the Loewner framework for FoS with delay. Finally, several numerical examples demonstrate the validity of our approach.
在本文中，我们通过应用洛埃纳矩阵方法，提出了一种用于线性分数阶系统（FoS）的数据驱动实现和模型降阶（MOR）方法。给定通过对FoS的传递函数进行采样获得的插值数据，以低计算成本构建与插值数据匹配的最小分数阶状态空间描述符模型。基于该框架，在分数阶系统的阶次α未知的情况下，通过求解关于样本数据的最小二乘优化问题来估计分数阶系统的等阶α。此外，我们针对具有延迟的FoS，在洛埃纳框架中使用插值方法提出了一个整数阶近似模型。最后，几个数值例子证明了我们方法的有效性。
