1. Reachable set bounding for neural networks with mixed delays: Reciprocally convex approach
- Author
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Yuxin Hou, Song Zhu, Ruihan Chen, and Yongqiang Qi
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Lemma (mathematics) ,Time Factors ,Artificial neural network ,Computer science ,Cognitive Neuroscience ,Uncertainty ,02 engineering and technology ,Upper and lower bounds ,Set (abstract data type) ,020901 industrial engineering & automation ,Artificial Intelligence ,Bounding overwatch ,0202 electrical engineering, electronic engineering, information engineering ,Humans ,Computer Simulation ,020201 artificial intelligence & image processing ,Convex combination ,Neural Networks, Computer ,Differentiable function ,Set estimation - 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.
- Published
- 2020