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research-article

A new look at the fractional initial value problem: the aberration phenomenon

[+] Author and Article Information
Yanting Zhao

Department of Automation, University of Science and Technology of China, Hefei, China, 230027
zyt9lsb@mail.ustc.edu.cn

YiHeng Wei

Department of Automation, University of Science and Technology of China, Hefei, China, 230027
neudawei@ustc.edu.cn

YuQuan Chen

Department of Automation, University of Science and Technology of China, Hefei, China, 230027
cyq@mail.ustc.edu.cn

Yong Wang

Department of Automation, University of Science and Technology of China, Hefei, China, 230027
yongwang@ustc.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4041621 History: Received June 03, 2018; Revised September 24, 2018

Abstract

A typical phenomenon of the fractional order system is presented to describe the initial value problem from a brand-new perspective. Firstly, several simulation examples are given to introduce the named aberration phenomenon, which reflects the complexity and the importance of the initial value problem. Then, generalizations on the infinite dimensional property and the long memory property are proposed to reveal the nature of the phenomenon. As a result, the relationship between the pseudo state-space model and the infinite dimensional exact state-space model is demonstrated. It shows the inborn defects of the initial values of the fractional order system. Afterward, the pre-initial process and the initialization function are studied. Finally, specific methods to estimate exact state-space models and fit initialization functions are proposed.

Copyright (c) 2018 by ASME
Topics: Simulation
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