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Design Verification for Control Engineering

  • Richard J. Boulton
  • Hanne Gottliebsen
  • Ruth Hardy
  • Tom Kelsey
  • Ursula Martin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2999)

Abstract

We introduce control engineering as a new domain of application for formal methods. We discuss design verification, drawing attention to the role played by diagrammatic evaluation criteria involving numeric plots of a design, such as Nichols and Bode plots. We show that symbolic computation and computational logic can be used to discharge these criteria and provide symbolic, automated, and very general alternatives to these standard numeric tests. We illustrate our work with reference to a standard reference model drawn from military avionics.

Keywords

Control Engineer Design Requirement Theorem Prove Symbolic Computation Computer Algebra System 
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.
    Arbib, M., Manes, E.: Machines in a category. SIAM review 57, 163–192 (1974)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Arthan, R., Caseley, P., O’Halloran, C., Smith, A.: ClawZ: Control laws in Z. In: Proc. 3rd IEEE International Conference on Formal Engineering Methods (ICFEM 2000), York (September 2000)Google Scholar
  3. 3.
    Boulton, R.J., Hardy, R., Martin, U.: A Hoare Logic for Single-Input Single-Output Continuous-Time Control Systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 113–125. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Cherlin, G.: Rings of continuous functions: decision problems. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 44–91. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dunstan, M., Kelsey, T., Martin, U., Linton, S.: Lightweight formal methods for computer algebra systems. In: ISSAC 1998: Proc. ACM International Symposium on Symbolic and Algebraic Computation, Rostock, ACM Press, New York (1998)Google Scholar
  7. 7.
    Martin, U., Dunstan, M., Kelsey, T., Linton, S.: Formal methods for extensions to computer algebra systems. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1758–1777. Springer, Heidelberg (1999)Google Scholar
  8. 8.
    Dutertre, B.: Elements of Mathematical Analysis in PVS. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 141–156. Springer, Heidelberg (1996)Google Scholar
  9. 9.
    Edalat, A., Lieutier, A.: Domain theory and differential calculus. In: Proc. IEEE LICS, vol. 17, IEEE Press, Los Alamitos (2002)Google Scholar
  10. 10.
    Robust Flight Control Design Challenge Problem Formulation and Manual: the High Incidence Research Model (HIRM) Garteur - Group for aeronautical research and technology in Europe Technical report, GARTEUR/TP-088-4 (1997)Google Scholar
  11. 11.
    Gordon, M.J.C.: Mechanizing programming logics in higher order logic. In: Birtwistle, G., Subrahmanyam, P.A. (eds.) Current Trends in Hardware Verification and Automated Theorem Proving, pp. 387–439. Springer, Heidelberg (1989)Google Scholar
  12. 12.
    Gottliebsen, H., Kelsey, T., Martin, U.: Hidden verification for computer algebra systems. Journal of Symbolic Computation (2004) (to appear)Google Scholar
  13. 13.
    Gottliebsen, H.: Transcendental Functions and Continuity Checking in PVS. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Gurr, C., Tourlas, K.: Towards the principled design of software engineering diagrams. In: Proc. 22nd International Conference on Software Engineering, pp. 509–520. ACM Press, New York (2000)Google Scholar
  15. 15.
    Harrison, J.: Theorem proving in the real numbers. Cambridge University Press, Cambridge (1995)Google Scholar
  16. 16.
    Hasegawa, M.: Models of Sharing Graphs. Springer, Heidelberg (1997)Google Scholar
  17. 17.
    Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12(10), 576–580, 583 (1969)zbMATHCrossRefGoogle Scholar
  18. 18.
    Jirstrand, M.: Nonlinear control system design by quantifier elimination. J. Symbolic Comput. 24, 137–152 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kalra, D., Barr, A.H.: Guaranteed Ray Intersections with Implicit Surfaces Computer Graphics (SIGGRAPH 1989 Proceedings), vol. 23(3), pp. 297–306 (1989)Google Scholar
  20. 20.
    Krogh, B.: Approximating Hybrid System Dynamics for Analysis and Control. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, p. 2. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  21. 21.
  22. 22.
  23. 23.
    Mahony, B.: The DOVE approach to the design of complex dynamic processes. In: Proc. of the First International Workshop on Formalising Continuous Mathematics, NASA conference publication NASA/CP-2002-211736, pp. 167–187 (2002)Google Scholar
  24. 24.
    Nipkow, T.: Hoare Logics in Isabelle/HOL. In: Proof and System-Reliability, pp. 341–367. Kluwer, Dordrecht (2002)Google Scholar
  25. 25.
    Ogata, K.: Modern Control Engineering, 3rd edn. Prentice-Hall, Englewood Cliffs (1997)Google Scholar
  26. 26.
    Pratt, R.W. (ed.): Flight Control Systems: Practical Issues in Design and Implementation. The Institution of Electrical Engineers. IEE Control Engineering Series, vol. 57 (2000)Google Scholar
  27. 27.
    Owre, S., Rushby, J., Shankar, N.: PVS: a prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)Google Scholar
  28. 28.
    Richardson, D.: Some Unsolvable Problems Involving Elementary Functions of a Real Variable. J. Symbolic Logic 33, 514–520 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Tiwari, A., Khanna, G.: Series of abstractions for hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, p. 465. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Richard J. Boulton
    • 1
  • Hanne Gottliebsen
    • 1
  • Ruth Hardy
    • 2
  • Tom Kelsey
    • 2
  • Ursula Martin
    • 1
  1. 1.Queen Mary University of London 
  2. 2.University of St Andrews 

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