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Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics

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Abstract

This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations. Firstly, the authors proposed “Consensus + Projection” flow with fractional order dynamics, which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms. Moreover, the authors prove that the proposed algorithm is convergent under certain iteration order and step-size. Furthermore, the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm. Finally, the authors illustrate the effectiveness of the proposed method with several numerical examples.

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Authors and Affiliations

  1. Anhui Engineering Laboratory of Human-Robot Integration System and Intelligent Equipment, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Wenqiang Yu, Songsong Cheng & Shuping He

Authors
  1. Wenqiang Yu
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  2. Songsong Cheng
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  3. Shuping He
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Corresponding author

Correspondence to Songsong Cheng.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 62103003, 62073001, and 61973002, the Anhui Provincial Key Research and Development Project under Grant 2022i01020013, the University Synergy Innovation Program of Anhui Province under Grant No. GXXT-2021-010, the Anhui Provincial Natural Science Foundation under Grant No. 2008085J32, the National Postdoctoral Program for Innovative Talents under Grant No. BX20180346, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2019M660834.

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Yu, W., Cheng, S. & He, S. Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics. J Syst Sci Complex 36, 613–631 (2023). https://doi.org/10.1007/s11424-023-1350-6

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  • DOI: https://doi.org/10.1007/s11424-023-1350-6

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