A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Yongpeng Tai, Ning Chen, Lijin Wang, Zaiyong Feng and Jun Xu
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Yongpeng Tai: College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China
Ning Chen: College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
Lijin Wang: College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
Zaiyong Feng: Department of Mathematics Teaching, Nanjing Institute of Railway Technology, Nanjing 210031, China
Jun Xu: College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China

Mathematics, 2020, vol. 8, issue 7, 1-13

Abstract: Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps.

Keywords: numerical method; fractional order; differential-algebraic equations; sliding mode control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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