Reachability analysis of complex planar hybrid systems
Journal article, 2013

Hybrid systems are systems that exhibit both discrete and continuous behavior. Reachability, the question of whether a system in one state can reach some other state, is undecidable for hybrid systems in general. In this paper we are concerned with GSPDIs, 2-dimensional systems generalizing SPDIs (planar hybrid systems based on "simple polygonal differential inclusions"), for which reachability have been shown to be decidable. GSPDIs are useful to approximate 2-dimensional control systems, allowing the verification of safety properties of such systems. In this paper we present the following two contributions: (i) an optimized algorithm that answers reachability questions for GSPDIs, where all cycles in the reachability graph are accelerated. (ii) An algorithm by which more complex planar hybrid automata are over-approximated by GSPDIs subject to two measures of precision. We prove soundness, completeness, and termination of both algorithms, and discuss their implementation.

Non-linear systems

Reachability checking

Safety verification

Differential inclusions

Hybrid systems

Author

Hallstein A. Hansen

University of South-Eastern Norway (USN)

Gerardo Schneider

University of Oslo

Chalmers, Computer Science and Engineering (Chalmers), Software Technology (Chalmers)

University of Gothenburg

M. Steffen

University of Oslo

Science of Computer Programming

0167-6423 (ISSN)

Vol. 78 12 2511-2536

Subject Categories

Embedded Systems

Control Engineering

Computer Systems

DOI

10.1016/j.scico.2013.02.007

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5/5/2021 6