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Ellipsoidal Techniques for Reachability Analysis

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Hybrid Systems: Computation and Control (HSCC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

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Abstract

This report describes the calculation of the reach sets and tubes for linear control systems with time-varying coefficients and hard bounds on the controls through tight external and internal ellipsoidal approximations. These approximating tubes touch the reach tubes from outside and inside respectively at every point of their boundary so that the surface of the reach tube is totally covered by curves that belong to the approximating tubes. The proposed approximation scheme induces a very small computational burden compared with other methods of reach set calculation.

In particular such approximations may be expressed through ordinary differential equations with coefficients given in explicit analytical form. This yields exact parametric representation of reach tubes through families of external and internal ellipsoidal tubes. The proposed techniques, combined with calculation of external and internal approximations for intersections of ellipsoids, provide an approach to reachability problems for hybrid systems.

Research supported by National Science Foundation Grant ECS 9725148

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Author information

Authors and Affiliations

  1. ERL, EECS, University of California at Berkeley, 195M Cory Hall, Berkeley, CA, 94720-1770

    Alexander B. Kurzhanski & Pravin Varaiya

Authors
  1. Alexander B. Kurzhanski
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  2. Pravin Varaiya
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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Kurzhanski, A.B., Varaiya, P. (2000). Ellipsoidal Techniques for Reachability Analysis. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_19

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  • DOI: https://doi.org/10.1007/3-540-46430-1_19

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  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

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