Improving SAT modulo ODE for hybrid systems analysis by combining different enclosure methods

Authors:
Andreas Eggers;Nacim Ramdani;Nedialko Nedialkov;Martin Fränzle
Affiliations:
Carl von Ossietzky Universität, Oldenburg, Germany;Université d'Orléans, PRISME, Bourges, France;McMaster University, Hamilton, Ontario, Canada;Carl von Ossietzky Universität, Oldenburg, Germany
Venue:
SEFM'11 Proceedings of the 9th international conference on Software engineering and formal methods
Year:
2011

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Abstract

Aiming at automatic verification and analysis techniques for hybrid systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art enclosure method for ODEs, and with bracketing systems which exploit monotonicity properties to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply our method to the analysis of a non-linear hybrid system by solving predicative encodings of an inductive stability argument and evaluate the impact of different methods and their combination.