Level Set Methods for Computing Reachable Sets of Hybrid Systems with Differential Algebraic Equation Dynamics

  • Ian M. Mitchell
  • Yoshihiko Susuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4981)


In previous work we demonstrated that reachability algorithms using level set methods and based on the Hamilton-Jacobi PDE can be adapted to systems whose dynamics are described by differential algebraic equations. Here we extend those results to hybrid systems. The only significant addition required is a mechanism for handling the state reset that occurs during discrete jumps between modes. We demonstrate the technique on a nonlinear power system voltage safety problem.


Hybrid System Hybrid Automaton Reachability Analysis Route Failure Discrete Jump 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mitchell, I.M.: Comparing forward and backward reachability as tools for safety analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 428–443. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Cross, E.A., Mitchell, I.M.: Level set methods for computing reachable sets of systems with differential algebraic equation dynamics. In: Proceedings of the American Control Conference, Seattle, WA (2008),
  3. 3.
  4. 4.
    Tomlin, C., Mitchell, I., Bayen, A., Oishi, M.: Computational techniques for the verification of hybrid systems. Proceedings of the IEEE 91(7), 986–1001 (2003)CrossRefGoogle Scholar
  5. 5.
    Venkatasubramanian, V., Schättler, H., Zaborszky, J.: Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. IEEE Transactions on Automatic Control 37(11), 1717–1733 (1992)zbMATHCrossRefGoogle Scholar
  6. 6.
    Susuki, Y., Hikihara, T.: Predicting voltage instability of power system via hybrid system reachability analysis. In: Proceedings of the American Control Conference, New York, NY, pp. 4166–4171 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ian M. Mitchell
    • 1
  • Yoshihiko Susuki
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Electrical EngineeringKyoto UniversityKyotoJapan

Personalised recommendations