Reachable set bounding for neural networks with mixed delays: Reciprocally convex approach.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date:

Abstract

This paper discusses the reachable set estimation problem of neural networks with mixed delays. Firstly, by means of the maximal Lyapunov-Krasovskii functional, we obtain a non-ellipsoid form of the reachable set. Further more, when calculating the derivative of the maximum Lyapunov functional, the lower bound lemma and reciprocally convex approach method are used to solve the reciprocally convex combination term, which reduce the related decision variables. Secondly, we extend the results to polytopic uncertainties neural networks and consider the case of uncertain differentiable parameters. Finally, two numerical examples and one application example are listed to show the validity of our methods.

Authors

  • Ruihan Chen
    School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China. Electronic address: crhcumt@163.com.
  • Song Zhu
    College of Sciences, China University of Mining and Technology, Xuzhou, 221116, China. Electronic address: songzhu82@gmail.com.
  • Yongqiang Qi
    School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China. Electronic address: qiyongqiang3@163.com.
  • Yuxin Hou
    School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China. Electronic address: 10173662@cumt.edu.cn.