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Non-uniqueness in Reverse Time of Hybrid System Trajectories

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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

Under standard Lipschitz conditions, trajectories of systems described by ordinary differential equations are well defined in both forward and reverse time. (The flow map is invertible.) However for hybrid systems, uniqueness of trajectories in forward time does not guarantee flow-map invertibility, allowing non-uniqueness in reverse time. The paper establishes a necessary and sufficient condition that governs invertibility through events. It is shown that this condition is equivalent to requiring reverse-time trajectories to transversally encounter event triggering hypersurfaces. This analysis motivates a homotopy algorithm that traces a one-manifold of initial conditions that give rise to trajectories which all reach a common point at the same time.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI, 53706

    Ian A. Hiskens

Authors
  1. Ian A. Hiskens
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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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© 2005 Springer-Verlag Berlin Heidelberg

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Hiskens, I.A. (2005). Non-uniqueness in Reverse Time of Hybrid System Trajectories. 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_22

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_22

  • 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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