SpaceEx: Scalable Verification of Hybrid Systems

Frehse, Goran; Guernic, Colas Le; Donzé, Alexandre; Cotton, Scott; Ray, Rajarshi; Lebeltel, Olivier; Ripado, Rodolfo; Girard, Antoine; Dang, Thao; Maler, Oded

doi:10.1007/978-3-642-22110-1_30

Cited by 707 publications

(707 citation statements)

References 14 publications

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“…Given the description of a hybrid system A, a safety property ϕ, and an abstract counter-example C as a sequence of modes/transitions, the falsification problem is reformulated as an optimization problem. The abstract counter-example C may be obtained by running the flowpipe construction tool such as SpaceEx [24], or alternatively by enumerating all likely mode/transition sequences up to a given length. Our implementation uses the latter combined with some user guidance to narrow the search space.…”

Section: A Implementationmentioning

confidence: 99%

“…Unfortunately, checking if a dynamical system (discrete, con- tinuous or hybrid) satisfies a safety property is undecidable for all but the simplest of cases. A number of verification tools for hybrid automata conservatively estimate the set of reachable behaviors (reach set estimation) for establishing safety properties of hybrid systems [4], [5], [12], [24], [30], [34], [36]. If the unsafe region is reachable, these techniques report a plausible abstract error trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…Likewise, the use of trajectory segments separated by different discrete modes allows us to naturally handle the discontinuities that arise through discrete transitions. Secondly, our approach also separates the search for an abstract violation that can be carried out using tools like SpaceEx [24] or Flow* [12] from the problem of concretizing these violations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Zutshi

Sankaranarayanan

Deshmukh³

et al. 2013

52nd IEEE Conference on Decision and Control

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Abstract-This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory.We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations.

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Section: A Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Zutshi

Sankaranarayanan

Deshmukh³

et al. 2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…The popular over-approximate representations are convex polytopes [9], ellipsoids [18], zonotopes [14] and support functions [19]. Along with their computation techniques, the tools CheckMate [23], Ellipsoidal Toolbox, PHAVer [11] and SpaceEx [12] are developed. On the other hand, few reachable set representations other than intervals (boxes) [21] are successfully applied to non-linear hybrid systems.…”

Section: Introductionmentioning

confidence: 99%

Flow* 1.2: More Effective to Play with Hybrid Systems

Chen¹,

Sankaranarayanan²,

Ábrahám³

EPiC Series in Computing

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This paper gives a brief overview of the new features introduced in the latest version of the tool Flow*. We mainly describe the new efficient scheme for integrating linear ODEs. We show that it can efficiently handle the challenging benchmarks on which, to the best of our knowledge, only SpaceEx works. Moreover, it is also possible to extend the method to deal with unbounded initial sets. A comparison between Flow* 1.2 and SpaceEx on those benchmarks is given. Besides, we also investigate the scalability of Flow* 1.2 based on our non-linear line circuit benchmarks.

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“…Both methods are provided by a proprietary package from Maplesoft [5]. Our experiments target the SpaceEx tool, which is a tool for verifying safety properties of linear hybrid systems [4]. SpaceEx allows the designer to specify a hybrid system and a property to be verified, in the form of a temporal logic formula.…”

Section: Introductionmentioning

confidence: 99%

Piecewise-Affine Approximations for a Powertrain Control Verification Benchmark

Deshmukh¹,

Ito²,

Jin³

et al.

EPiC Series in Computing

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We present a benchmark example of an automotive powertrain control system converted to a hybrid system with piecewise-affine (PWA) continuous dynamics. The purpose is to provide an example of an industrial nonlinear system that is amenable to existing software tools for performing verification of safety properties for hybrid systems. Existing algorithmic approaches to hybrid system verification require that system representations are restricted to specific classes of models. Therefore, it is important to develop and evaluate techniques to generate approximate models that adhere to the required class of systems without introducing an unacceptable amount of approximation errors. The example we present is intended to demonstrate a symbolic method to automatically approximate a nonlinear model with a PWA approximation while respecting a given bound on the approximation error. While existing tools are applicable to the resulting model, the scale of the PWA model is intended to challenge the capabilities of these tools. We conduct an experimental comparison between the original and PWA models and present our observations and discuss challenges for the research community.

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SpaceEx: Scalable Verification of Hybrid Systems

Cited by 707 publications

References 14 publications

A trajectory splicing approach to concretizing counterexamples for hybrid systems

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Flow* 1.2: More Effective to Play with Hybrid Systems

Piecewise-Affine Approximations for a Powertrain Control Verification Benchmark

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