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Automotive control revisited linear inequalities as approximation of reachable sets

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Abstract

Reachability analysis of hybrid system imposes restrictions on the continuous and discrete behavior. In this paper a method is proposed to approximate the reachable set of linear systems by linear inequalities. It allows to use the full continuous dynamics of hybrid systems for reachability analysis. This method is applied to an automotive control problem, which was presented by Stauner et al. in [SMF97].

Research supported by Netherlands Organization for Scientific Research (NWO) under contract SION 612-14-004

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References

  1. [ACH+95] R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.

    Google Scholar 

  2. David Burghes and Alexander Graham. Introduction to Control Theory, including Optimal Control. Ellis Horwood series in mathematics and its applications. John Wiley & Sons, New York, 1980.

    Google Scholar 

  3. Roger W. Brockett. Finite Dimensional Linear Systems. John Wiley & Sons, New York, 1970.

    Google Scholar 

  4. E. Dolginova and N. Lynch. Safety verification for automated platoon maneuvers: A case study. In Oded Maler, editor, HART'97, LNCS 1201. Springer-Verlag, 1997.

    Google Scholar 

  5. Gerd Fischer. Analytische Geometrie. Friedr. Vieweg & Sohn, Braunschweig, 1991.

    Google Scholar 

  6. Philip E. Gill, Walter Murray, and Margaret H. Wright. Numerical Linear Algebra and Optimization, volume 1. Addison-Wesley, 1991.

    Google Scholar 

  7. T.A. Henzinger and P.-H. Ho. Algorithmic analysis of nonlinear hybrid systems. In P. Wolper, editor, CA V 95: Computer-aided Verification, LNCS 939, pages 225–238. Springer-Verlag, 1995.

    Google Scholar 

  8. L. Helmink, M.P.A. Sellink, and F.W. Vaandrager. Proof-checking a data link protocol. In H. Barendregt and T. Nipkow, editors, Proceedings International Workshop TYPES'93, Nijmegen, The Netherlands, May 1993, LNCS 806, pages 127–165. Springer-Verlag, 1994. Full version available as CWI technical report.

    Google Scholar 

  9. T.A. Henzinger and H. Wong-Toi. Linear phase-portrait approximations for nonlinear hybrid systems. In R. Alur, T.A. Henzinger, and E.D. Sontag, editors, Hybrid Systems III, LNCS 1066, pages 377–388. Springer-Verlag, 1996.

    Google Scholar 

  10. E.B. Lee and L. Markus. Foundations of optimal control theory. The SIAM series in applied mathematics. Wiley, New York, 1967.

    Google Scholar 

  11. N. Lynch, R. Segala, F.W. Vaandrager, and H.B. Weinberg. Hybrid I/O automata. In R. Alur, T. Henzinger, and E. Sontag, editors, Hybrid Systems III, LNCS 1066, pages 496–510. Springer-Verlag, 1996.

    Google Scholar 

  12. A. Puri, V. Borkar, and P. Varaiya. ε-approximation of differential inclusions. In Proceedings of the 34th IEEE Conference on Decision and Control (CDC 95), 1995.

    Google Scholar 

  13. Alexander Schrijver. Theory of Linear and Integer Programming. John Wiley & Sons, 1986.

    Google Scholar 

  14. Thomas Stauner, Olaf Müller, and Max Fuchs. Using hytech to verify an automotive control system. In Oded Maler, editor, HART'97, LNCS 1201, pages 139–153. Springer-Verlag, 1997.

    Google Scholar 

  15. Thomas Stauner. Specification and Verification of an Electronic Height Control System using Hybrid Automata. Master's thesis, Munich University of Technology, 1997.

    Google Scholar 

  16. Li Xuandong, Dang Van Hung, and Zheng Tao. Checking hybrid automata for linear duration invariants. In ASIAN' 97, LNCS 1345, pages 166–180. Springer-Verlag, 1997.

    Google Scholar 

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Thomas A. Henzinger Shankar Sastry

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© 1998 Springer-Verlag Berlin Heidelberg

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Fehnker, A. (1998). Automotive control revisited linear inequalities as approximation of reachable sets. In: Henzinger, T.A., Sastry, S. (eds) Hybrid Systems: Computation and Control. HSCC 1998. Lecture Notes in Computer Science, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64358-3_35

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  • DOI: https://doi.org/10.1007/3-540-64358-3_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64358-6

  • Online ISBN: 978-3-540-69754-1

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