Abstract
We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose right-hand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required differential invariants. As a means for combining local differential invariants into global system invariants in a sound way, our fixedpoint algorithm works with a compositional verification logic for hybrid systems. To improve the verification power, we further introduce a saturation procedure that refines the system dynamics successively with differential invariants until safety becomes provable. By complementing our symbolic verification algorithm with a robust version of numerical falsification, we obtain a fast and sound verification procedure. We verify roundabout maneuvers in air traffic management and collision avoidance in train control.
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Platzer, A., Clarke, E.M. (2008). Computing Differential Invariants of Hybrid Systems as Fixedpoints. In: Gupta, A., Malik, S. (eds) Computer Aided Verification. CAV 2008. Lecture Notes in Computer Science, vol 5123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70545-1_17
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DOI: https://doi.org/10.1007/978-3-540-70545-1_17
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