Carnegie Mellon University
Browse
file.pdf (491.02 kB)

Computing differential invariants of hybrid systems as fixedpoints

Download (491.02 kB)
journal contribution
posted on 2005-08-01, 00:00 authored by Andre Platzer, E. M. Clarke

Abstract: "We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations that have right-hand sides that are polynomials in the state variables. In order to verify non-trivial 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."

History

Publisher Statement

All Rights Reserved

Date

2005-08-01

Usage metrics

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC