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Level Set Methods for Computation in Hybrid Systems

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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

Reachability analysis is frequently used to study the safety of control systems. We present an implementation of an exact reachability operator for nonlinear hybrid systems. After a brief review of a previously presented algorithm for determining reachable sets and synthesizing control laws—upon whose theory the new implementation rests—an equivalent formulation is developed of the key equations governing the continuous state reachability. The new formulation is implemented using level set methods, and its effectiveness is shown by the numerical solution of three examples.

Research supported by DARPA under the Software Enabled Control Program (AFRL contract F33615-99-C-3014), and by a Frederick E. Terman Faculty Award.

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Author information

Authors and Affiliations

  1. Scientific Computing and Computational Mathematics Program, Gates 2B, Stanford University, Stanford, CA, 94305

    Ian Mitchell

  2. Department of Aeronautics and Astronautics, 250 Durand, Stanford University, Stanford, CA, 94305

    Claire J. Tomlin

Authors
  1. Ian Mitchell
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  2. Claire J. Tomlin
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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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© 2000 Springer-Verlag Berlin Heidelberg

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Mitchell, I., Tomlin, C.J. (2000). Level Set Methods for Computation in Hybrid Systems. 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_27

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  • DOI: https://doi.org/10.1007/3-540-46430-1_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

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