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Comparing Forward and Backward Reachability as Tools for Safety Analysis

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Hybrid Systems: Computation and Control (HSCC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4416))

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Abstract

Using only the existence and uniqueness of trajectories for a generic dynamic system with inputs, we define and examine eight types of forward and backward reachability constructs. If the input is treated in a worst-case fashion, any forward or backward reach set or tube can be used for safety analysis, but if the input is treated in a best-case fashion only the backward reach tube always provides the correct results. Fortunately, forward and backward algorithms can be exchanged if well-posed reverse time trajectories can be defined. Unfortunately, backward reachability constructs are more likely to suffer from numerical stability issues, especially in systems with significant contraction—the very systems where forward simulation and reachability are most effective.

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, 2366 Main Mall, Vancouver, BC, V6T 1Z4, Canada

    Ian M. Mitchell

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  1. Ian M. Mitchell
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Alberto Bemporad Antonio Bicchi Giorgio Buttazzo

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Mitchell, I.M. (2007). Comparing Forward and Backward Reachability as Tools for Safety Analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_34

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  • DOI: https://doi.org/10.1007/978-3-540-71493-4_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71492-7

  • Online ISBN: 978-3-540-71493-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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