Discrete-time neural network with two classes of bias noises for solving time-variant matrix inversion and application to robot tracking

  • Peng Miao
  • Deyu Wu
  • Yanjun Shen
  • Zhiqiang Zhang
Original Article


It is well known that noise is inevitable in real world, especially in the case of solving time-variant matrix inversion. Therefore, it is more necessary to study the algorithm with bias noises to solve time-variant matrix inversion. This paper investigates discrete-time neural network with two classes of bias noises for solving time-variant matrix inversion, and its application to robot tracking based on the property of second-order differential equation. Firstly, the model is presented and some indispensable propaedeutics are given. Then, continuous-time and discrete-time neural network with two classes of bias noises is designed, respectively. Their convergence and finite-time stability are also theoretically analyzed. Finally, the proposed models are applied to a five-link robot tracking. Numerical simulations demonstrate the superiority and effectiveness of our method.


Discrete-time neural network Time-variant matrix inversion Bias noises Robot tracking 



This work was supported by the National Science Foundation of China (61374028), the Key Scientific Research Foundation of Education Bureau of Henan Province, China (Grant No. 19A140021), and the 2016 Social science and economics’ association research topics in Henan Province (SKL-2016-3868). The paper has not been published and will not be submitted elsewhere for publication. In order to improve the quality of the article, with the consent of the original author and Zhiqiang Zhang, we invited Zhiqiang Zhang to revise the article. He added the finite-time stability to the revised paper.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Basic CoursesZhengzhou College of Science & TechnologyZhengzhouChina
  2. 2.College of Electrical Engineering and New EnergyChina Three Gorges UniversityYichangChina
  3. 3.General Education CentreZhengzhou Business UniversityGongyiChina

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