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Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

  • Andrew Sogokon
  • Paul B. Jackson
  • Taylor T. Johnson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10227)

Abstract

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.

Keywords

Hybrid System Safety Property Reachable State Drill String Discrete Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors wish to thank to the anonymous reviewers for their careful reading and valuable suggestions for improving this paper.

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Authors and Affiliations

  1. 1.Institute for Software Integrated SystemsVanderbilt UniversityNashvilleUSA
  2. 2.Laboratory for Foundations of Computer ScienceUniversity of EdinburghEdinburghScotland, UK

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