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Fully-Automated Verification of Linear Systems Using Reachability Analysis with Support Functions

Authors:

Mark Wetzlinger,

Niklas Kochdumper,

Matthias AlthoffAuthors Info & Claims

HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

Article No.: 5, Pages 1 - 12

https://doi.org/10.1145/3575870.3587121

Published: 09 May 2023 Publication History

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Abstract

While reachability analysis is one of the major techniques for formal verification of dynamical systems, the requirement to adequately tune algorithm parameters often prevents its widespread use in practical applications. In this work, we fully automate the verification process for linear time-invariant systems: Based on the computation of tight upper and lower bounds for the support function of the reachable set along a given direction, we present a fully-automated verification algorithm, which is based on iterative refinement of the upper and lower bounds and thus always returns the correct result in decidable cases. While this verification algorithm is particularly well suited for cases where the specifications are represented by halfspace constraints, we extend it to arbitrary convex unsafe sets using the Gilbert-Johnson-Keerthi algorithm. In summary, our automated verifier is applicable to arbitrary convex initial sets, input sets, as well as unsafe sets, can handle time-varying inputs, automatically returns a counterexample in case of a safety violation, and scales to previously unanalyzable high-dimensional state spaces. Our evaluation on several challenging benchmarks shows significant improvements in computational efficiency compared to verification using other state-of-the-art reachability tools.

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Cited By

Gupta LChowdhury Choton JPrabhakar P(2024)Safety Verification of Closed-loop Control System with Anytime Perception2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10611044(227-233)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10611044
Wetzlinger MKochdumper NBak SAlthoff M(2023)Fully Automated Verification of Linear Systems Using Inner and Outer Approximations of Reachable SetsIEEE Transactions on Automatic Control10.1109/TAC.2023.329200868:12(7771-7786)Online publication date: Dec-2023
https://doi.org/10.1109/TAC.2023.3292008
Gaßmann VAlthoff M(2023)Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust RegionsIEEE Open Journal of Control Systems10.1109/OJCSYS.2023.33013352(310-324)Online publication date: 2023
https://doi.org/10.1109/OJCSYS.2023.3301335

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cover image ACM Conferences

HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

May 2023

239 pages

ISBN:9798400700330

DOI:10.1145/3575870

Copyright © 2023 ACM.

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Published: 09 May 2023

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Cited By

Gupta LChowdhury Choton JPrabhakar P(2024)Safety Verification of Closed-loop Control System with Anytime Perception2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10611044(227-233)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10611044
Wetzlinger MKochdumper NBak SAlthoff M(2023)Fully Automated Verification of Linear Systems Using Inner and Outer Approximations of Reachable SetsIEEE Transactions on Automatic Control10.1109/TAC.2023.329200868:12(7771-7786)Online publication date: Dec-2023
https://doi.org/10.1109/TAC.2023.3292008
Gaßmann VAlthoff M(2023)Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust RegionsIEEE Open Journal of Control Systems10.1109/OJCSYS.2023.33013352(310-324)Online publication date: 2023
https://doi.org/10.1109/OJCSYS.2023.3301335

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