Reachability analysis of complex planar hybrid systems
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. (C) 2013 Elsevier B.V. All rights reserved.
hybrid systems differential inclusions reachability checking safety verification non-linear systems