Benchmark: A Nonlinear Reachability Analysis Test Set from Numerical Analysis

9 pages•Published: December 17, 2015

Hoang-Dung Tran, Luan Viet Nguyen and Taylor T Johnson

Abstract

The field of numerical analysis has developed numerous benchmarks for evaluating differential and algebraic equation solvers. In this paper, we describe a set of benchmarks commonly used in numerical analysis that may also be effective for evaluating continuous and hybrid systems reachability and verification methods. Many of these examples are challenging and have highly nonlinear differential equations and upwards of tens of dimensions (state variables). Additionally, many examples in numerical analysis are originally encoded as differential algebraic equations (DAEs) with index greater than one or as implicit differential equations (IDEs), which are challenging to model as hybrid automata. We present executable models for ten benchmarks from a test set for initial value problems (IVPs) in the SpaceEx format (allowing for nonlinear equations instead of restricting to affine) and illustrate their conversion to several other formats (dReach, Flow*, and the MathWorks Simulink/Stateflow [SLSF]) using the HyST tool. For some instances, we present successful analysis results using dReach and SLSF.

Keyphrases: academic, benchmark, hybrid automata, nonlinear differential algebraic equations, nonlinear ordinary differential equations, reachability

In: Goran Frehse and Matthias Althoff (editors). ARCH14-15. 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems, vol 34, pages 89-97.

Links:	https://easychair.org/publications/paper/714m
	https://doi.org/10.29007/6dcf

BibTeX entry

@inproceedings{ARCH15:Benchmark_Nonlinear_Reachability_Analysis,
  author    = {Hoang-Dung Tran and Luan Viet Nguyen and Taylor T Johnson},
  title     = {Benchmark: A Nonlinear Reachability Analysis Test Set from Numerical Analysis},
  booktitle = {ARCH14-15. 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {34},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/714m},
  doi       = {10.29007/6dcf},
  pages     = {89-97},
  year      = {2015}}

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