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Automating Verification of Cooperation, Control, and Design in Traffic Applications

  • Werner Damm
  • Alfred Mikschl
  • Jens Oehlerking
  • Ernst-Rüdiger Olderog
  • Jun Pang
  • André Platzer
  • Marc Segelken
  • Boris Wirtz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4700)

Abstract

We present a verification methodology for cooperating traffic agents covering analysis of cooperation strategies, realization of strategies through control, and implementation of control. For each layer, we provide dedicated approaches to formal verification of safety and stability properties of the design. The range of employed verification techniques invoked to span this verification space includes application of pre-verified design patterns, automatic synthesis of Lyapunov functions, constraint generation for parameterized designs, model-checking in rich theories, and abstraction refinement. We illustrate this approach with a variant of the European Train Control System (ETCS), employing layer specific verification techniques to layer specific views of an ETCS design.

Keywords

Hybrid System Lyapunov Function Linear Matrix Inequality Discrete Transition Drive Train 
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.

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References

  1. 1.
    Alur, R., Grosu, R., Hur, Y., Kumar, V., Lee, I.: Modular specification of hybrid systems in CHARON. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 6–19. Springer, Heidelberg (2000)Google Scholar
  2. 2.
    Alur, R., Grosu, R., Lee, I., Sokolsky, O.: Compositional modeling and refinement for hierarchical hybrid systems. Journal of Logic and Algebraic Programming 68(1-2), 105–128 (2006)zbMATHCrossRefGoogle Scholar
  3. 3.
    Balluchi, A., Benvenuti, L., Engell, S., Geyer, T., Johansson, K., Lamnabhi-Lagarrigue, F., Lygeros, J., Morari, M., Papafotiou, G., Sangiovanni-Vincentelli, A., Santucci, F., Stursberg, O.: Hybrid control of networked embedded systems. European Journal on Control, Fundam. Issues in Control 11(4-5), 478–508 (2006)Google Scholar
  4. 4.
    Beckert, B., Giese, M., Hähnle, R., Klebanov, V., Rümmer, P., Schlager, S., Schmitt, P.H.: The KeY System 1.0 (deduction component). In: Pfenning, F. (ed.) CADE 2007. LNCS, vol. 4603, Springer, Heidelberg (2007)Google Scholar
  5. 5.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  6. 6.
    Bohn, J., Damm, W., Klose, J., Moik, A., Wittke, H.: Modeling and validating train system applications using Statemate and live sequence charts. In: Proc. Conference on Integrated Design and Process Technology. Society for Design and Process Science (2002)Google Scholar
  7. 7.
    Borchers, B.: CSDP, a C library for semidefinite programming. Optimization Methods and Software 10(1), 613–623 (1999)CrossRefGoogle Scholar
  8. 8.
    Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. In: SIAM (1994)Google Scholar
  9. 9.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control 43(4) (1998)Google Scholar
  10. 10.
    Cervin, A., Henriksson, D., Lincoln, B., Eker, J., Arzén, K.: How does control timing affect performance? IEEE Control Systems Magazine 23(2), 16–30 (2003)CrossRefGoogle Scholar
  11. 11.
    Damm, W., Disch, S., Hungar, H., Jacobs, S., Pang, J., Pigorsch, F., Scholl, C., Waldmann, U., Wirtz, B.: Exact state set representations in the verification of linear hybrid systems with large discrete state space. Technical report, AVACS (2007)Google Scholar
  12. 12.
    Damm, W., Disch, S., Hungar, H., Pang, J., Pigorsch, F., Scholl, C., Waldmann, U., Wirtz, B.: Automatic verification of hybrid systems with large discrete state space. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 276–291. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Damm, W., Hungar, H., Olderog, E.-R.: Verification of cooperating traffic agents. International Journal of Control 79(5), 395–421 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. International Journal of Foundations of Computer Science 18(1), 63–86 (2007)zbMATHCrossRefGoogle Scholar
  15. 15.
    Donde, V., Hiskens, I.A.: Shooting methods for locating grazing phenomena in hybrid systems. Intern. Journal of Bifurcation and Chaos 16(3), 671–692 (2006)CrossRefGoogle Scholar
  16. 16.
    Feng, G.: Stability analysis of piecewise discrete-time linear systems. IEEE Transactions on Automatic Control 47(7), 1108–1112 (2002)CrossRefGoogle Scholar
  17. 17.
    Franklin, G.F., Powell, J.D., Workman, M.: Digital Control of Dynamic Systems. Pearson, London (1998)Google Scholar
  18. 18.
    Fränzle, M., Herde, C.: HySAT: An efficient proof engine for bounded model checking of hybrid systems. Formal Methods in System Design 30(3), 179–198 (2007)zbMATHCrossRefGoogle Scholar
  19. 19.
    Frehse, G.: Compositional verification of hybrid systems with discrete interaction using simulation relations. In: Proc. 13th IEEE Conference on Computer Aided Control Systems Design, IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  20. 20.
    Frehse, G.: Compositional Verification of Hybrid Systems using Simulation Relations. PhD thesis, Radboud Universiteit Nijmegen (2005)Google Scholar
  21. 21.
    Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)Google Scholar
  22. 22.
    Hager, G.: European ACAS operational evaluation – Final report. Technical Report EEC Report No. 316, Eurocontrol (1997)Google Scholar
  23. 23.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  24. 24.
    Haxthausen, A.E., Peleska, J.: Formal development and verification of a distributed railway control system. IEEE Transactions on Software Engineering 26(8), 687–701 (2000)CrossRefGoogle Scholar
  25. 25.
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. 11th IEEE Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  26. 26.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control 43(5), 540–554 (1998)zbMATHCrossRefGoogle Scholar
  27. 27.
    Henzinger, T.A., Horowitz, B., Majumdar, R., Wong-Toi, H.: Beyond HyTech: Hybrid systems analysis using interval numerical methods. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 130–144. Springer, Heidelberg (2000)Google Scholar
  28. 28.
    Johansson, M., Rantzer, A.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Transactions on Automatic Control 43 (1998)Google Scholar
  29. 29.
    Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall, Englewood Cliffs (1996)Google Scholar
  30. 30.
    Kratz, F., Sokolsky, O., Pappas, G.J., Lee, I.: R-Charon, a modeling language for reconfigurable hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 392–406. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  31. 31.
    Leveson, N.G.: Safeware: System Safety and Computers. Addison-Wesley, Reading (1995)Google Scholar
  32. 32.
    Livadas, C., Lygeros, J., Lynch, N.A.: High-level modeling and analysis of TCAS. Proceedings of IEEE – Special Issue on Hybrid Systems: Theory & Applications 88(7), 926–947 (2000)Google Scholar
  33. 33.
    Lofberg, J.: YALMIP: a toolbox for modeling and optimization in Matlab. In: IEEE Intern. Symp. Computer Aided Control Systems Design, pp. 284–289. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  34. 34.
    Loos, R., Weispfenning, V.: Applying linear quantifier elimination. The Computer Journal 36(5), 450–462 (1993)zbMATHCrossRefGoogle Scholar
  35. 35.
    Lyapunov, M.A.: Problème général de la stabilité du movement. Ann. Fac. Sci. Toulouse. 9, 203–474 (1907), (Translation of a paper published in Comm. Soc. Math. Kharkow, 1893, reprinted Ann. Math. Studies No. 17, Princeton Univ. Press (1949)Google Scholar
  36. 36.
    Lygeros, J., Godbole, D.N., Sastry, S.S.: Verified hybrid controllers for automated vehicles. IEEE Transactions on Automatic Control 43(4), 522–539 (1998)zbMATHCrossRefGoogle Scholar
  37. 37.
    Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata revisited. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 403–417. Springer, Heidelberg (2001)Google Scholar
  38. 38.
    Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata. Information and Computation 185(1), 105–157 (2003)zbMATHCrossRefGoogle Scholar
  39. 39.
    Mishchenko, A., Chatterjee, S., Jiang, R., Brayton, R.K.: FRAIGs: A unifying representation for logic synthesis and verification. Technical report, EECS Dept., UC Berkeley (2005)Google Scholar
  40. 40.
    Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming. In: SIAM (1994)Google Scholar
  41. 41.
    Oehlerking, J., Burchardt, H., Theel, O.: Fully automated stability verification for piecewise affine systems. In: Buttazzo, G., Bemporad, A., Bicchi, A. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 741–745. Springer, Heidelberg (2007)Google Scholar
  42. 42.
    Pettersson, S.: Analysis and Design of Hybrid Systems. PhD thesis, Chalmers University of Technology, Gothenburg (1999)Google Scholar
  43. 43.
    Platzer, A.: Differential dynamic logic for verifying parametric hybrid systems. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS, vol. 4548, Springer, Heidelberg (2007)Google Scholar
  44. 44.
    Platzer, A.: Differential logic for reasoning about hybrid systems. In: Buttazzo, G., Bemporad, A., Bicchi, A. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 746–749. Springer, Heidelberg (2007)Google Scholar
  45. 45.
    Platzer, A.: A temporal dynamic logic for verifying hybrid system invariants. In: Proc. International Symposium on Logical Foundations of Computer Science. LNCS, vol. 4514, pp. 457–471. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  46. 46.
    Platzer, A.: Towards a hybrid dynamic logic for hybrid dynamic systems. In: Blackburn, P., Bolander, T., Braüner, T., de Paiva, V., Villadsen, J. (eds.) Proc. LICS Intern. Workshop on Hybrid Logic. ENTCS (2007)Google Scholar
  47. 47.
    Platzer, A., Clarke, E.M.: The image computation problem in hybrid systems model checking. In: Proc. 10th Workshop on Hybrid Systems: Computation and Control. LNCS, vol. 4416, pp. 473–486. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  48. 48.
    Segelken, M.: Abstraction and counterexample-guided construction of omega-automata for model checking of step-discrete linear hybrid models. In: Proc. 19th Conference on Computer Aided Verification. LNCS, Springer, Heidelberg (2007)Google Scholar
  49. 49.
    Silva, B.I., Richeson, K., Krogh, B.H., Chutinan, A.: Modeling and verification of hybrid dynamical system using CheckMate. In: Proc. 4th Conference on Automation of Mixed Processes (2000)Google Scholar
  50. 50.
    Somenzi, F., Bloem, R.: Efficient Büchi Automata from LTL Formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  51. 51.
    Stauner, T.: Systematic Development of Hybrid Systems. PhD thesis, Technische Universität München (2001)Google Scholar
  52. 52.
    Stauner, T.: Discrete-time refinement of hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 407–420. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  53. 53.
    Tomlin, C., Pappas, G.J., Sastry, S.S.: Conflict resolution for air traffic management: A case study in multi-agent hybrid systems. IEEE Transactions on Automatic Control 43(4), 509–521 (1998)zbMATHCrossRefGoogle Scholar
  54. 54.
    Wende, D.: Fahrdynamik des Schienenverkehrs. Teubner (2003)Google Scholar
  55. 55.
    Yakubovich, V.: S-procedure in nonlinear control theory. Vestnik Leningrad University, pp. 62–71 (1971)Google Scholar
  56. 56.
    Zhou, C., Hansen, M.: Duration Calculus: A Formal Approach to Real-Time Systems. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  57. 57.
    Zhou, C., Hoare, C., Ravn, A.P.: A calculus of durations. Information Processing Letters 40(5), 269–276 (1991)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Werner Damm
    • 1
    • 2
  • Alfred Mikschl
    • 1
  • Jens Oehlerking
    • 1
  • Ernst-Rüdiger Olderog
    • 1
  • Jun Pang
    • 1
  • André Platzer
    • 1
  • Marc Segelken
    • 2
  • Boris Wirtz
    • 1
  1. 1.Carl von Ossietzky Universität Oldenburg, Ammerländer Heerstraße 114-118, 26111 OldenburgGermany
  2. 2.OFFIS, Escherweg 2, 26121 OldenburgGermany

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