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Interval observer design of dynamical systems with neural networks

Published: 19 May 2021 Publication History

Abstract

This paper proposes an interval observer design method to construct lower-bound and upper-bound of system state trajectories in run time. The developed interval observer consists of two auxiliary neural networks derived from the neural network in dynamical systems, and two observer gains to ensure the positivity and the convergence of the corresponding error dynamics. Particularly, if the neural network is driven by the output of the system, the developed approach contains a promising neural-network-free design feature. The developed method is validated with evaluations on an adaptive cruise control system with a neural network controller.

References

[1]
Denis Efimov and Tarek Raïssi. 2016. Design of interval observers for uncertain dynamical systems. Automation and Remote Control 77, 2 (2016), 191--225.
[2]
Jean-Luc Gouzé, Alain Rapaport, and Mohamed Zakaria Hadj-Sadok. 2000. Interval observers for uncertain biological systems. Ecological modelling 133, 1--2 (2000), 45--56.
[3]
Hoang-Dung Tran, Xiaodong Yang, Diego Manzanas Lopez, Patrick Musau, Luan Viet Nguyen, Weiming Xiang, Stanley Bak, and Taylor T. Johnson. 2020. NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems. In Computer Aided Verification, Shuvendu K. Lahiri and Chao Wang (Eds.). Springer International Publishing, Cham, 3--17.
[4]
Weiming Xiang, Hoang-Dung Tran, Xiaodong Yang, and Taylor T Johnson. 2020, Reachable set estimation for neural network control systems: a simulation-guided approach. IEEE Transactions on Neural Networks and Learning Systems (2020.

Cited By

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  • (2022)RNN-based Observability Analysis for Magnetometer-Free Sparse Inertial Motion Tracking2022 25th International Conference on Information Fusion (FUSION)10.23919/FUSION49751.2022.9841375(1-8)Online publication date: 4-Jul-2022

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  1. Interval observer design of dynamical systems with neural networks

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    cover image ACM Conferences
    HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control
    May 2021
    300 pages
    ISBN:9781450383394
    DOI:10.1145/3447928
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 19 May 2021

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    Author Tags

    1. dynamical systems
    2. interval observer
    3. neural networks
    4. runtime monitoring

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    HSCC '21 Paper Acceptance Rate 27 of 77 submissions, 35%;
    Overall Acceptance Rate 153 of 373 submissions, 41%

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    • (2022)RNN-based Observability Analysis for Magnetometer-Free Sparse Inertial Motion Tracking2022 25th International Conference on Information Fusion (FUSION)10.23919/FUSION49751.2022.9841375(1-8)Online publication date: 4-Jul-2022

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