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Conic Abstractions for Hybrid Systems

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Formal Modeling and Analysis of Timed Systems (FORMATS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10419))

Abstract

Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of bounded-time reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems.

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Acknowledgments

This work was partly supported by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award) and by the ARC project DP140104219 (Robust AI Planning for Hybrid Systems).

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Authors and Affiliations

  1. Australian National University, Canberra, Australia

    Sergiy Bogomolov

  2. IST Austria, Klosterneuburg, Austria

    Sergiy Bogomolov, Mirco Giacobbe, Thomas A. Henzinger & Hui Kong

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  1. Sergiy Bogomolov
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  2. Mirco Giacobbe
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  3. Thomas A. Henzinger
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  4. Hui Kong
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Corresponding authors

Correspondence to Mirco Giacobbe or Hui Kong .

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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Dept. d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gilles Geeraerts

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Bogomolov, S., Giacobbe, M., Henzinger, T.A., Kong, H. (2017). Conic Abstractions for Hybrid Systems. In: Abate, A., Geeraerts, G. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2017. Lecture Notes in Computer Science(), vol 10419. Springer, Cham. https://doi.org/10.1007/978-3-319-65765-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-65765-3_7

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