Advertisement

Flow*: An Analyzer for Non-linear Hybrid Systems

  • Xin Chen
  • Erika Ábrahám
  • Sriram Sankaranarayanan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8044)

Abstract

The tool Flow* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. Flow* combines well-known Taylor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. Flow* supports a wide variety of optimizations including adaptive step sizes, adaptive selection of approximation orders and the heuristic selection of template directions for aggregating flowpipes. This paper describes Flow* and demonstrates its performance on a series of non-linear continuous and hybrid system benchmarks. Our comparisons show that Flow* is competitive with other tools.

Keywords

Hybrid System Discrete Transition Taylor Model Adaptive Step Adaptive Step Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Berz, M.: Modern Map Methods in Particle Beam Physics. Advances in Imaging and Electron Physics, vol. 108. Academic Press (1999)Google Scholar
  2. 2.
    Berz, M., Makino, K.: Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliable Computing 4, 361–369 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fainekos, G., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410, 4262–4291 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, X., Ábrahám, E., Sankaranarayanan, S.: Taylor model flowpipe construction for non-linear hybrid systems. In: Proc. RTSS 2012, pp. 183–192. IEEE (2012)Google Scholar
  5. 5.
    Makino, K., Berz, M.: Taylor models and other validated functional inclusion methods. J. Pure and Applied Mathematics 4(4), 379–456 (2003)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Neher, M., Jackson, K.R., Nedialkov, N.S.: On Taylor model based integration of ODEs. SIAM Journal on Numerical Analysis 45, 236–262 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Frehse, G., et al.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer (2010)Google Scholar
  9. 9.
    Benvenuti, L., Bresolin, D., Casagrande, A., Collins, P., Ferrari, A., Mazzi, E., Sangiovanni-Vincentelli, A., Villa, R.: Reachability computation for hybrid systems with Ariadne. In: Proc. the 17th IFAC World Congress. IFAC Papers-OnLine (2008)Google Scholar
  10. 10.
    Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. Journal on Satisfiability, Boolean Modeling and Computation 1, 209–236 (2007)Google Scholar
  11. 11.
    Nedialkov, N.S.: Implementing a rigorous ode solver through literate programming. In: Modeling, Design, and Simulation of Systems with Uncertainties Mathematical Engineering, vol. 3, pp. 3–19. Springer (2011)Google Scholar
  12. 12.
    She, Z., Xue, B., Zheng, Z.: Algebraic analysis on asymptotic stability of continuous dynamical systems. In: Proc. ISSAC 2011, pp. 313–320. ACM (2011)Google Scholar
  13. 13.
    Craciun, G., Tang, Y., Feinberg, M.: Understanding bistability in complex enzyme-driven reaction networks. Proc. of the National Academy of Sciences 103(23), 8697–8702 (2006)CrossRefzbMATHGoogle Scholar
  14. 14.
    Klipp, E., Herwig, R., Kowald, A., Wierling, C., Lehrach, H.: Systems Biology in Practice: Concepts, Implementation and Application. Wiley-Blackwell (2005)Google Scholar
  15. 15.
    Vilar, J.M.G., Kueh, H.Y., Barkai, N., Leibler, S.: Mechanisms of noise-resistance in genetic oscillators. Proc. of the National Academy of Sciences 99(9), 5988–5992 (2002)CrossRefGoogle Scholar
  16. 16.
    Fehnker, A., Ivančić, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xin Chen
    • 1
  • Erika Ábrahám
    • 1
  • Sriram Sankaranarayanan
    • 2
  1. 1.RWTH Aachen UniversityGermany
  2. 2.University of ColoradoBoulderUSA

Personalised recommendations