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Safety verification of finite real-time nonlinear hybrid systems using enhanced group preserving scheme

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Abstract

In recent years, finite realtime nonlinear hybrid systems(FRNHS) have been widely used in the fields of biology, chemical control, embedded systems, etc. Its safety verification becomes more and more important. Compared with traditional hybrid systems, the safety verification of FRNHS is decidable, but the computational accuracy of its reach set demands higher. Group preserving scheme(GPS) achieves better accuracy and stabilization than traditional numerical algorithms due to its inherent properties in Minkowski space. This paper creatively applies GPS into the safety verification of FRNHS. Based on Euler method and GPS, we put forward the corresponding enhanced algorithms, which make the numerical computational accuracy higher. Through the experiment, the errors introduced by four various numerical computation methods are compared. The experimental results indicate that the proposed enhanced GPS in this paper has higher accuracy and can effectively make safety verification for FRNHS within the \(\epsilon \text {-}\)error approximation.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11371003 and 11461006, the Natural Science Foundation of Guangxi under Grant No. 2012GXNSFGA060003 and the Scientific Research Project No. 201012MS274 from Guangxi Education Department. The authors also want to thank the anonymous reviewers for their advice on improving this paper.

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Authors and Affiliations

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

    Hui Zhang

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

    Hui Zhang

  3. Guizhou Bank Postdoctoral Station, Guiyang, 550001, China

    Hui Zhang

  4. Guangxi Key Laboratory of Hybrid Computational and IC Design Analysis, Guangxi University for Nationalities, Guangxi, 530006, China

    Jinzhao Wu

  5. Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, 550025, China

    Jianguang Lu

  6. School of Computer Science and Educational Software, Guangzhou University, Guangzhou, 510006, China

    Juan Tang

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  1. Hui Zhang
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  2. Jinzhao Wu
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  3. Jianguang Lu
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  4. Juan Tang
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Correspondence to Jinzhao Wu.

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Zhang, H., Wu, J., Lu, J. et al. Safety verification of finite real-time nonlinear hybrid systems using enhanced group preserving scheme. Cluster Comput 19, 2189–2199 (2016). https://doi.org/10.1007/s10586-016-0652-z

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