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A Fixed-time Distributed Algorithm for Least Square Solutions of Linear Equations

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  • Control Theory and Applications
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Abstract

This study presents a fixed-time convergent algorithm to achieve distributed least square (DLS) solutions of networked linear equations. Each agent in the network only knows a subset of the equations and can only exchange messages with its nearest neighbors. Unlike finite-time counterparts, the settling time of the fixed-time distributed algorithm does not depend upon the initial states, and can be preassigned according to the requirements of the task. Numerical simulations verify the theoretical results.

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Authors and Affiliations

  1. College of Science and also with the Center for Data Analysis and Algorithm Technology, Guilin University of Technology, Guilin, 541004, China

    Shuling Li, Wu Ai & Quanxi Feng

  2. School of Computer and Information, Anqing Normal University, Anqing, 246011, China

    Jian Wu

Authors
  1. Shuling Li
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  2. Wu Ai
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  3. Jian Wu
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  4. Quanxi Feng
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Corresponding author

Correspondence to Wu Ai.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Xian-Ming Zhang under the direction of Editor PooGyeon Park. This work was supported by the National Natural Science Foundation of China (Nos. 61703117, 61603003 and 61763008), Natural Science Foundation of Guangxi (No. 2017GXNSFBA198113) and the Foundation of Guilin University of Technology (GLUTQD2007029).

Shuling Li received her B.S. degree in applied statistics from Jiaying University, Meizhou, China, in 2018. She is currently pursuing an M.S. degree in statistics at Guilin University of technology, Guilin, China. She mainly focuses on the area of distributed machine learning.

Wu Ai received his B.S. degree in mathematics and applied mathematics from Hubei University for Nationalities, Enshi, China, in 2005, an M.S. degree in computational mathematics from Huazhong University of Science and Technology, Wuhan, China, in 2007, and a Ph.D. degree in applied mathematics from Xidian University, Xi’an, China, in 2017. He was a Visiting Scholar with La Trobe University, Melbourne, Australia, from 2018 to 2019. He is currently an Associate Professor with the College of Science, Guilin University of Technology, Guilin, China. His current research interests include distributed optimization, machine learning, and multi-agent systems.

Jian Wu received his Ph.D. degree in applied mathematics from Xidian University, Xi’an, China, in 2015. He is currently an Associate Professor with the School of Computer and Information, Anqing Normal University, Anqing, China. His current research interests include intelligent control, adaptive control, and adaptive switching control.

Quanxi Feng received his Ph.D. degree in applied mathematics from Xidian University, Xi’an, China, in 2014. He is currently an Associate Professor with the College of Science, Guilin University of Technology, Guilin, China. His current research interests include computational intelligence and machine learning in real world.

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Li, S., Ai, W., Wu, J. et al. A Fixed-time Distributed Algorithm for Least Square Solutions of Linear Equations. Int. J. Control Autom. Syst. 19, 1311–1318 (2021). https://doi.org/10.1007/s12555-020-0096-3

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  • DOI: https://doi.org/10.1007/s12555-020-0096-3

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