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Controlling Control Systems: An Application of Evolving Retrenchment

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ZB 2002:Formal Specification and Development in Z and B (ZB 2002)

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Abstract

We review retrenchment as a liberalisation of refinement, for the description of applications too rich (e.g. using continuous and infinite types) for refinement. A specialisation of the notion, evolving retrenchment, is introduced, motivated by the need for an approximate, evolving notion of simulation. The focus of the paper is the case study, a substantial second-order linear control system. The design step from continuous to zero-order hold discrete system is expressible as an evolving retrenchment. Thus we demonstrate that the retrenchment approach can formalise the development of useful applications, which are outside the scope of refinement. The work is presented in a data type-enriched language containing the B language of J.-R. Abrial.

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Author information

Authors and Affiliations

  1. Department of Computing, Open University, Walton Hall, MK7 6AA, Milton Keynes, UK

    Michael Poppleton

  2. Department of Computer Science, Manchester University, M13 9PL, Manchester, UK

    Richard Banach

Authors
  1. Michael Poppleton
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  2. Richard Banach
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Editor information

Editors and Affiliations

  1. Laboratoire LSR, IMAG, CNRS, 681,rue de la Passerelle, 38402, Saint Martin d’Hères Cedex, France

    Didier Bert

  2. SCISM, Centre for Applied Fromal Methods, SouthBank University, Borough Road, SE1 0AA, London, UK

    Jonathan P. Bowen

  3. Department of Computer Science, University of Essex, Wivenhoe Park, CO4 3SQ, Colchester, UK

    Martin C. Henson

  4. CAESER, The School of Computer Science and Engineering, The University of New South Wales, UNSW, 2052, Sydney, NSW, Australia

    Ken Robinson

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© 2002 Springer-Verlag Berlin Heidelberg

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Poppleton, M., Banach, R. (2002). Controlling Control Systems: An Application of Evolving Retrenchment. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds) ZB 2002:Formal Specification and Development in Z and B. ZB 2002. Lecture Notes in Computer Science, vol 2272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45648-1_3

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  • DOI: https://doi.org/10.1007/3-540-45648-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43166-4

  • Online ISBN: 978-3-540-45648-3

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