Advertisement

Synthesizing Switching Logic Using Constraint Solving

  • Ankur Taly
  • Sumit Gulwani
  • Ashish Tiwari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5403)

Abstract

A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property. By construction, the synthesized hybrid system is well-formed and is guaranteed safe. Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem. When the system, the safety property, and the controlled invariant are all expressed only using polynomials, the generated constraint is an ∃ ∀ formula in the theory of reals, which we solve using SMT solvers. The generated controlled invariant is then used to arrive at the maximally liberal switching logic.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(3), 3–34 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Asarin, E., Bournez, O., Dang, T., Maler, O., Pnueli, A.: Effective synthesis of switching controllers for linear systems. Proc. IEEE 88(7), 1011–1025 (2000)CrossRefGoogle Scholar
  3. 3.
    Blanchini, F.: Set invariance in control. Automatica 35, 1747–1767 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Burns, K., Gidea, M.: Differential Geometry and Topology: With a view to dynamical systems. Chapman & Hall, Boca Raton (2005)zbMATHGoogle Scholar
  5. 5.
    Colón, M.: Schema-guided synthesis of imperative programs by constraint solving. In: LOPSTR, pp. 166–181 (2004)Google Scholar
  6. 6.
    Cury, J., Brogh, B., Niinomi, T.: Supervisory controllers for hybrid systems based on approximating automata. IEEE Trans. Aut. Control 43, 564–568 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gulwani, S., Tiwari, A.: Constraint-based approach for analysis of hybrid systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 190–203. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Koo, T., Sastry, S.: Mode switching synthesis for reachability specification. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 333–346. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Manon, P., Valentin-Roubinet, C.: Controller synthesis for hybrid systems with linear vector fields. In: Proc. IEEE Symp. on Intell. Control, pp. 17–22 (1999)Google Scholar
  10. 10.
    Moor, T., Raisch, J.: Discrete control of switched linear systems. In: Proc. Eur. Control Conf. ECC 1999 (1999)Google Scholar
  11. 11.
    Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 477–492. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Sankaranarayanan, S., Sipma, H., Manna, Z.: Constructing invariants for hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 539–554. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Tomlin, C., Lygeros, L., Sastry, S.: A game-theoretic approach to controller design for hybrid systems. Proc. of the IEEE 88(7), 949–970 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ankur Taly
    • 1
  • Sumit Gulwani
    • 2
  • Ashish Tiwari
    • 3
  1. 1.Computer Science Dept.Stanford UniversityUSA
  2. 2.Microsoft ResearchRedmond
  3. 3.SRI InternationalMenlo Park

Personalised recommendations