Computing Differential Invariants of Hybrid Systems as Fixedpoints

  • André Platzer
  • Edmund M. Clarke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5123)


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.


verification of hybrid systems differential invariants verification logic fixedpoint engine 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • André Platzer
    • 1
  • Edmund M. Clarke
    • 2
  1. 1.Department of Computing ScienceUniversity of OldenburgGermany
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityPittsburgh

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