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Computing flow pipe of embedded hybrid systems using deep group preserving scheme

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Abstract

In this paper, we propose a novel methodology of numerical approximation to analyze flow of a nonlinear embedded hybrid system. For proving that all trajectories of a hybrid system do not enter an unsafe region, many classic numerical approaches such as Euler, Runge–Kutta methods for ordinary differential equations (ODEs) are applied, whereas, there exist several defects, including so-called spurious solutions and ghost fixed points. Moreover, to approximate the proper solution as much as possible, step size selection becomes especially important. In comparison, integrating group preserving scheme (GPS) which calculates true circumstance getting rid of spurious solutions and ghost fixed points, with neural network model which reduces numerical errors, deep GPS (DGPS) eliminates aforementioned adverse factors and gains better numerical approximation using a large time step size. The experimental results show that the proposed method makes safety verification for an embedded hybrid system well.

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Funding

This research is supported by the National Natural Science Foundation of China under Grant No. 61772006, the Science and Technology Major Project of Guangxi under Grant No. AA17204096, the Key Research and Development Project of Guangxi under Grant No. AB17129012, and the Special Fund for Bagui Scholars of Guangxi.

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Authors and Affiliations

  1. Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu, 610041, Sichuan, China

    Zhenxing Xu & Jinzhao Wu

  2. University of Chinese Academy of Sciences, Beijing, Beijing, 100049, China

    Zhenxing Xu & Jinzhao Wu

  3. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, Guangxi, China

    Jinzhao Wu

Authors
  1. Zhenxing Xu
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  2. Jinzhao Wu
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Contributions

ZX developed the theoretical formalism, performed the analytic calculations and performed the numerical simulations. Both ZX and JW authors contributed to the final version of the manuscript. JW supervised the project.

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Correspondence to Zhenxing Xu.

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Hereby, we consciously assure that for the manuscript “Safety Verification of Embedded Hybrid Systems Using Deep Group Preserving Scheme” the following is fulfilled:

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Xu, Z., Wu, J. Computing flow pipe of embedded hybrid systems using deep group preserving scheme. Cluster Comput 25, 1207–1220 (2022). https://doi.org/10.1007/s10586-021-03495-x

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