Safety Verification of Hybrid Systems by Constraint Propagation Based Abstraction Refinement

Ratschan, Stefan; She, Zhikun

doi:10.1007/978-3-540-31954-2_37

Cited by 84 publications

(60 citation statements)

References 20 publications

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“…To evaluate the integrated tool and the influence of the different enclosure methods, we apply our solver to the twotank model from [25], which has been frequently used as a case study for verification tools cf., e.g., [10,22]. This system comprises two tanks connected by a tube.…”

Section: Two-tank Systemmentioning

confidence: 99%

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

et al. 2012

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Aiming at automatic verification and analysis techniques for hybrid discrete-continuous systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art interval solver for ODEs, and with bracketing systems, which exploit monotonicity properties allowing to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply the combined iSAT-ODE solver to the analysis of a variety of non-linear hybrid systems by solving predicative encodings of reachability properties and of an inductive stability argument, and evaluate the impact of the different enclosure methods, decision heuristics and their combination. Our experiments include classic benchmarks A preliminary version of this paper appeared in [6]. from the literature, as well as a newly-designed conveyor belt system that combines hybrid behavior of parallel components, a slip-stick friction model with non-linear dynamics and flow invariants and several dimensions of parameterization. In the paper, we also present and evaluate an extension of VNODE-LP tailored to its use as a deduction mechanism within iSAT-ODE, to allow fast re-evaluations of enclosures over arbitrary subranges of the analyzed time span.

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Section: Two-tank Systemmentioning

confidence: 99%

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

et al. 2012

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“…HSolver [18,19] is dedicated to the safety analysis for nonlinear hybrid systems. This include ODE driven dynamical systems.…”

Section: Comparison With Hsolvermentioning

confidence: 99%

The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Collins

Goldsztejn

2008

Electronic Notes in Theoretical Computer Science

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This paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In continuous time, this algorithm is called the Reach and Evolve algorithm. The Reach and Evolve algorithm is based on interval analysis and a rigorous discretization of space and time. Promising numerical experiments are presented.

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“…In the future work, we plan to improve our step size control and use better single step algorithm. We plan to use the method in the hybrid system safety verification Algorithm [25].…”

Section: Resultsmentioning

confidence: 99%

“…Such enclosures are needed in some applications, for example in systems verification [13,25], or in theorem provers [6,27].…”

mentioning

confidence: 99%

Rigorous integration of non-linear ordinary differential equations in chebyshev basis

Dzetkulič

2014

Numer Algor

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In this paper, we introduce a new approach to multiple step verified integration of non-linear ordinary differential equations. The approach is based on the technique of a Taylor model integration, however, a novel method is introduced to suppress the wrapping effect over several integration steps. This method is simpler and more robust compared to the known methods. It allows more general inputs, while it does not require rigorous matrix inversion. Moreover, our integration algorithm allows the use of various types of underlying function enclosures. We present rigorous arithmetic operations with function enclosures based on the truncated Chebyshev series. Computational experiments are used to show the wrapping effect suppression of our method and to compare integration algorithm that uses Chebyshev function enclosures with the existing algorithms that use function enclosures based on the truncated Taylor series (Taylor models).

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Safety Verification of Hybrid Systems by Constraint Propagation Based Abstraction Refinement

Cited by 84 publications

References 20 publications

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Rigorous integration of non-linear ordinary differential equations in chebyshev basis

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