Model checking polygonal differential inclusions using invariance kernels. (English) Zbl 1202.68254

Steffen, Bernhard (ed.) et al., Verification, model checking, and abstract interpretation. 5th international conference, VMCAI 2004, Venice, Italy, January 11–13, 2004. Proceedings. Berlin: Springer (ISBN 3-540-20803-8/pbk). Lect. Notes Comput. Sci. 2937, 110-121 (2004).
Summary: Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. Here, we identify and compute an important object of such systems’ phase portrait, namely invariance kernels. An invariant set is a set of initial points of trajectories which keep rotating in a cycle forever and the invariance kernel is the largest of such sets. We show that this kernel is a non-convex polygon and we give a non-iterative algorithm for computing the coordinates of its vertices and edges. Moreover, we present a breadth-first search algorithm for solving the reachability problem for such systems. Invariance kernels play an important role in the algorithm.
For the entire collection see [Zbl 1031.68005].


68Q60 Specification and verification (program logics, model checking, etc.)


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