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Primal–Dual Tests for Safety and Reachability

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Hybrid Systems: Computation and Control (HSCC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3414))

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Abstract

A methodology for safety verification using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from convex duality and the concept of density functions, in this paper we show that reachability can also be verified through convex programming. Several convex programs for verifying safety, reachability, and other properties such as eventuality are formulated. Some examples are provided to illustrate their applications.

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Author information

Authors and Affiliations

  1. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, 91125, USA

    Stephen Prajna

  2. Department of Automatic Control, Lund Institute of Technology, SE 221 00, Lund, Sweden

    Anders Rantzer

Authors
  1. Stephen Prajna
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  2. Anders Rantzer
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Editor information

Editors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Manfred Morari

  2. Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland

    Lothar Thiele

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Prajna, S., Rantzer, A. (2005). Primal–Dual Tests for Safety and Reachability. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_35

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25108-8

  • Online ISBN: 978-3-540-31954-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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