03014ntm a22003257a 4500003000800000005001700008008004100025040000800066100002000074245006900094260002200163500001100185505001300196505002000209505002100229505002500250505001900275505002000294505002600314505002000340505005800360505003700418505006700455505005300522505005900575505001900634505001700653520197600670856004202646AT-ISTA20200722172852.0200722s2019 au ||||| m||| 00| 0 eng d cIST aGiacobbe, Mirco aAutomatic time-unbounded reachability analysis of hybrid systems bIST Austriac2019 aThesis aAbstract aAcknowledgments aAbout the Author aList of Publications aList of Tables aList of Figures aList of Abbreviations a1. Introduction a2. Template-polyhedral Abstraction of Hybrid Automata a3. Automatic Template Refinement a4. Counterexample-guided Refinement for Convex Hybrid Automata a5. Conic Abstractions for Affine Hybrid Automata a6. Space-Time Interpolation for Affine Hybrid Automata a7. Conclusions aBibliography aHybrid automata combine finite automata and dynamical systems, and model the interaction of digital with physical systems. Formal analysis that can guarantee the safety of all behaviors or rigorously witness failures, while unsolvable in general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking, assisted theorem proving. Nevertheless, very few methods have addressed the time-unbounded reachability analysis of hybrid automata and, for current sound and automatic tools, scalability remains critical. We develop methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion. We use template polyhedra, i.e., polyhedra whose facets are normal to a given set of directions. While, previously, directions were given by the user, we introduce (1) the first method for computing template directions from spurious counterexamples, so as to generalize and eliminate them. The method applies naturally to convex hybrid automata, i.e., hybrid automata with (possibly non-linear) convex constraints on derivatives only, while for linear ODE requires further abstraction. Specifically, we introduce (2) the conic abstractions, which, partitioning the state space into appropriate (possibly non-uniform) cones, divide curvy trajectories into relatively straight sections, suitable for polyhedral abstractions. Finally, we introduce (3) space-time interpolation, which, combining interval arithmetic and template refinement, computes appropriate (possibly non-uniform) time partitioning and template directions along spurious trajectories, so as to eliminate them. We obtain sound and automatic methods for the reachability analysis over dense and unbounded time of convex hybrid automata and hybrid automata with linear ODE. We build prototype tools and compare—favorably—our methods against the respective state-of-the-art tools, on several benchmarks. uhttps://doi.org/10.15479/AT:ISTA:6894