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Non-linear Continuous Systems for Safety Verification

10 pagesPublished: February 1, 2017


Safety verification of hybrid dynamical systems relies crucially on the ability to reason about reachable sets of continuous systems whose evolution is governed by a system of ordinary differential equations (ODEs). Verification tools are often restricted to handling a particular class of continuous systems, such as e.g. differential equations with constant right-hand sides, or systems of affine ODEs. More recently, verification tools capable of working with non-linear differential equations have been developed. The behavior of non-linear systems is known to be in general extremely difficult to analyze because solutions are rarely available in closed-form. In order to assess the practical utility of the various verification tools working with non-linear ODEs it is very useful to maintain a set of verification problems. Similar efforts have been successful in other communities, such as automated theorem proving, SAT solving and numerical analysis, and have accelerated improvements in the tools and their underlying algorithms. We present a set of 65 safety verification problems featuring non-linear polynomial ODEs and for which we have proofs of safety. We discuss the various issues associated with benchmarking the currently available verification tools using these problems.

Keyphrases: benchmark, continuous systems, nonlinear systems, ordinary differential equations, Polynomial dynamics, reachability, safety, verification

In: Goran Frehse and Matthias Althoff (editors). ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems, vol 43, pages 42--51

BibTeX entry
  author    = {Andrew Sogokon and Khalil Ghorbal and Taylor T Johnson},
  title     = {Non-linear Continuous Systems for Safety Verification},
  booktitle = {ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {43},
  pages     = {42--51},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/w94n}}
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