Efficient Dynamic Error Reduction for Hybrid Systems Reachability Analysis

Schupp, Stefan; Ábrahám, Erika

doi:10.1007/978-3-319-89963-3_17

Cited by 12 publications

(5 citation statements)

References 20 publications

(23 reference statements)

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“…A similar approach adaptively tunes all algorithm parameters without backtracking while respecting an error bound related to the Hausdorff distance between the exact reachable set and the computed enclosure [54]. While the desired error bound still has to be manually specified for the aforementioned approaches, automated verification algorithms automatically refine this error bound until the specification can be either proven or disproven: Brute-force approaches [9,50] simply re-compute the reachable set with improved algorithm parameter values. The framework of counterexample-guided abstraction refinement (CEGAR) automatically refines the model [26,53] or the set representation [12,13].…”

Section: Related Workmentioning

confidence: 99%

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

Wetzlinger

Kochdumper

Bak

et al. 2023

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

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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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Section: Related Workmentioning

confidence: 99%

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

Wetzlinger

Kochdumper

Bak

et al. 2023

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

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“…In [27] the authors propose an efficient Counterexample-Guided Abstraction Refinement (CEGAR) based approach to dynamically reduce overapproximation error. The idea, albeit similar to ours, is to automatically select suitable parameters of the reachability algorithm, so that verification can be performed more efficiently and accurately.…”

Section: Related Workmentioning

confidence: 99%

Dynamics-aware subspace identification for decomposed aggregation in the reachability analysis of hybrid automata

Hakim

Bekooij

2020

Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

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Hybrid automata are an emerging formalism used to model sampled-data control Cyber-Physical Systems (CPS), and analyze their behavior using reachability analysis. This is because hybrid automata provide a richer and more flexible modeling framework, compared to traditional approaches. However, modern state-of-the-art tools struggle to analyze such systems, due to the computational complexity of the reachability algorithm, and due to the introduced overapproximation error. These shortcomings are largely attributed (but not limited) to the aggregation of sets.In this paper we propose a subspace identification approach for decomposed aggregation in the reachability analysis of hybrid automata with linear dynamics. Our key contribution is the observation that the choice of a good subspace basis does not only depend on the sets being aggregated, but also on the continuous-time dynamics of an automaton. With this observation in mind, we present a dynamics-aware subspace identification algorithm that we use to construct tight decomposed convex hulls for the aggregated sets.Our approach is evaluated on two practically relevant hybrid automata models of sampled-data CPS that have been shown to be difficult to analyze by modern state-ofthe-art tools. Specifically, we show that for these models our approach can improve the accuracy of the reachable set by up-to 10 times when compared to standard Principal Component Analysis (PCA), for which finding a fixed point is not guaranteed. We also show that while the computational complexity is increased, a fixed-point is found earlier.

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“…Then these representations change over the course of the algorithm into further overapproximations during steps 2 and 3, and as a result amplify the error. Furthermore the error scales with the dimensionality of the system and certain representations become less tight when variables with simple dynamics are mixed into the state-space, such as clocks and Piece-Wise Constant (PWC) variables [23,24]. Finally, when simple guard and invariant constraints are defined for e.g.…”

Section: Common Issuesmentioning

confidence: 99%

Reachability Analysis of Hybrid Automata with Clocked Linear Dynamics

Hakim

Bekooij

2019

Proceedings of the 22nd International Workshop on Software and Compilers for Embedded Systems

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Disributed control systems often exhibit aperiodic sampling behavior due to varying communication delays and execution times. In such cases traditional analysis methods fall short because the functional and temporal behaviors need to be analyzed simultaneously. Therefore such systems are often modeled by Hybrid Automata (HA) with clock and non-clock variables, and verified using reachability analysis. However, modern reachability tools introduce a large overapproximation error because non-clock variables, as well as clock variables, are equally treated by the algorithm.In this paper we present a reachability algorithm which exploits the explicit separation of clock and non-clock variables in the Hybrid Automata with Clocked Linear Dynamics (HA-CLD) subclass, as well as restricting that guard and invariant constraints can only be specified in the HA-CLD model for clock variables. These properties of HA-CLD allow independent computation of tight reachable set overapproximations, in the form of flow-pipes, of clock and nonclock variables. A computationaly efficient and tight intersection operation is obtained by relating segments of the clock flow-pipe with segments of the non-clock flow-pipe.We demonstrate the effectiveness of our approach using two benchmarks, in the context of verifying stability. From the results it can be concluded that our reachability approach obtains significantly tighter results with an up-to 65 times smaller run-time compared to the start-of-the-art model checker SpaceEx.

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Efficient Dynamic Error Reduction for Hybrid Systems Reachability Analysis

Cited by 12 publications

References 20 publications

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

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

Dynamics-aware subspace identification for decomposed aggregation in the reachability analysis of hybrid automata

Reachability Analysis of Hybrid Automata with Clocked Linear Dynamics

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