Skip to main content

Logic and Control

  • Conference paper
Book cover Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

Included in the following conference series:

Abstract

I will give a brief account of how I came to introduce the term Hybrid System and to encourage it as a subject of study. I will also discuss what one should understand to pursue the subject fully, and also discuss the lines of development of my joint research with Wolf Kohn in this area. This is an area at the interface of mathematics, computer science, and control engineering, which has been pursued by many in all three areas since its inception. It can be thought of as the subject which deals with the interaction of discrete and continuous processes. This paper is intended to be legible to those without advanced analysis or differential geometry in their background. We concentrate on control, not on logics of hybrid systems, and aim at an audience unfamiliar with control. I make no apologies for not being technical. This is not a survey of the field. For a year 2000 survey see [1]. A survey made now would be very large.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Davoren, J.M., Nerode, A.: Logics for Hybrid Systems. Proceedings of the IEEE 88(7), 985–1010 (2000)

    Article  Google Scholar 

  2. Hybrid control systems. Antsaklis, P.J., Nerode, A. (eds.) IEEE Transactions Automatic Control 43, no. 4. Institute of Electrical and Electronics Engineers, Inc (1998)

    Google Scholar 

  3. Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.): Hybrid Systems. LNCS, vol. 736. Springer, Heidelberg (1993)

    Google Scholar 

  4. Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds.): Hybrid systems II. Papers from the Third Workshop held at Cornell University. LNCS, vol. 999, pp. 28–30. Springer, Heidelberg (1995)

    Google Scholar 

  5. Alur, R., Sontag, E.D., Henzinger, T.A. (eds.): Hybrid Systems III. LNCS, vol. 1066. Springer, Heidelberg (1996)

    Google Scholar 

  6. Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds.): Hybrid Systems IV. LNCS, vol. 1273. Springer, Heidelberg (1997)

    Google Scholar 

  7. Antsaklis, P., Kohn, W., Nerode, A., Lemmon, M., Sastry, S. (eds.): Hybrid Systems V. LNCS, vol. 1567. Springer, Heidelberg (1999)

    Google Scholar 

  8. Kohn, W.: A Declarative Theory for Rational Controllers. Proceedings of the 27th IEEE Conference on Decision and Control 1, 131–136 (1988)

    Google Scholar 

  9. Kohn, W., Brayman, V., Cholewinski, P., Nerode, A.: Hybrid systems as Finsler manifolds: finite state control as approximation to connections. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S.S. (eds.) Hybrid Systems II. LNCS, vol. 999, Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  10. Kohn, W., Brayman, V., Cholewinski, P., Nerode, A.: Control in Hybrid Systems, International Journal of Hybrid Systems 3 (2003)

    Google Scholar 

  11. Kohn, W., Brayman, V., Nerode, A.: Control Synthesis in Hybrid Systems with Finsler Dynamics, Houston Journal of Mathematics vol. 28(2), pp. 353–375

    Google Scholar 

  12. Nerode, A.: Modeling Intelligent Control. In: Proc. DARPA Workshop on Software Tools for the Domain Specific Software Initiative, Pacifica, Ca (July 17-19, 1990)

    Google Scholar 

  13. Kohn, W., Nerode, A.: Parallel Computer Architectures. LNCS, vol. 732. Springer, Heidelberg (1993)

    Google Scholar 

  14. Kohn, W., Nerode, A., Remmel, J.B.: Continualization: A Hybrid Systems Control Technique for Computing, In: Proceedings of CESA’96 IMACS Multiconference, vol 2. pp. 507–511

    Google Scholar 

  15. Diaz, A.: Extraction of Finite State Controllers, AD and DA maps, and Associated Small Topologies for Measure Valued Control Laws International Journal of Hybrid Systems (September 2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nerode, A. (2007). Logic and Control. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_61

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73001-9_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics