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Verifying safety and persistence properties of hybrid systems using flowpipes and continuous invariants

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Original languageEnglish
Title of host publicationNASA Formal Methods
Subtitle of host publication9th International Symposium, NFM 2017, Moffett Field, CA, USA, May 16-18, 2017, Proceedings
PublisherSpringer, Cham
Number of pages15
ISBN (Electronic)978-3-319-57288-8
ISBN (Print)978-3-319-57287-1
Publication statusE-pub ahead of print - 9 Apr 2017
Event9th NASA Formal Methods Symposium - Moffett Field, United States
Duration: 16 May 201718 May 2017

Publication series

NameLecture Notes in Computer Science
PublisherSpringer, Cham
ISSN (Print)0302-9743


Conference9th NASA Formal Methods Symposium
Abbreviated titleNFM 2017
CountryUnited States
CityMoffett Field
Internet address


We propose a method for verifying persistence of nonlinear hybrid systems. Given some system and an initial set of states, the method can guarantee that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flow-pipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study concerning showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flow-pipes or just reasoning about invariants alone can be insufficient. The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property with the aid of an automatic prover specifically designed for handling transcendental functions.


9th NASA Formal Methods Symposium


Moffett Field, United States

Event: Conference

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