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A Hoare Logic for Single-Input Single-Output Continuous-Time Control Systems

  • Richard J. Boulton
  • Ruth Hardy
  • Ursula Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2623)

Abstract

This paper presents a Hoare-style logic for reasoning about the frequency response of control systems in the continuous-time domain. Two properties, the gain (amplitude) and phase shift, of a control system are considered. These properties are for a sinusoidal input of variable frequency. The logic operates over a simplified form of block diagram, including arbitrary transfer functions, feedback loops, and summation of signals. Reasoning is compositional, i.e. properties of a system can be deduced from properties of its subsystems. A prototype tool has been implemented in a mechanised theorem prover.

Keywords

Transfer Function Phase Shift Predicate Logic Hybrid Automaton Sequencing Rule 
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.
    R. Arthan, P. Caseley, C. O’Halloran, and A. Smith. ClawZ: Control laws in Z. In Proc. 3rd IEEE International Conference on Formal Engineering Methods (ICFEM 2000), York, September 2000.Google Scholar
  2. 2.
    M. J. C. Gordon. Mechanizing programming logics in higher order logic. In G. Birtwistle and P. A. Subrahmanyam, editors, Current Trends in Hardware Veri fication and Automated Theorem Proving, pages 387–439. Springer-Verlag, 1989.Google Scholar
  3. 3.
    C. A. R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12(10):576–580, 583, October 1969.zbMATHCrossRefGoogle Scholar
  4. 4.
    The MathWorks. Simulink. http://www.mathworks.com/products/simulink/Google Scholar
  5. 5.
    B. Mahony. 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 pages 167–187 August 2002Google Scholar
  6. 6.
    T. Nipkow. Hoare Logics in Isabelle/HOL. In Proof and System-Reliability, pages 341–367, Kluwer, 2002.Google Scholar
  7. 7.
    K. Ogata. Modern Control Engineering. Prentice-Hall, third edition, 1997.Google Scholar
  8. 8.
    R. W. Pratt, editor. Flight Control Systems: Practical Issues in Design and Implementation,volume 57 of IEE Control Engineering Series. The Institution of Electrical Engineers, 2000. Copublished by The American Institute of Aeronautics and Astronautics.Google Scholar
  9. 9.
    A. Tiwari and G. Khanna. Series of abstractions for hybrid automata. In Proc. 5th International Workshop on Hybrid Systems: Computation and Control (HSCC 2002), volume 2289 of Lecture Notes in Computer Science, Springer, 2002.CrossRefGoogle Scholar
  10. 10.
    C. Gurr and K. Tourlas. Towards the principled design of software engineering diagrams. In Proc. 22nd International Conference on Software Engineering, pages 509–520, ACM Press, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Richard J. Boulton
    • 1
  • Ruth Hardy
    • 1
  • Ursula Martin
    • 1
  1. 1.School of Computer ScienceUniversity of St AndrewsScotlandUK

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