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Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants

Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants
Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants
We describe a method for verifying the temporal property of persistence in non-linear hybrid systems. Given some system and an initial set of states, the method establishes 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 flowpipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study 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 flowpipes or just reasoning about invariants alone can be insufficient and shows the richness of systems that one can handle with the proposed method, since the systems features modes with non-polynomial ODEs. We also propose an alternative method for proving persistence that relies solely on flowpipe computation.
0168-7433
1005-1029
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Jackson, Paul B.
8c57df38-6cb2-488d-afec-b154d3ddf1cc
Johnson, Taylor T.
204159bb-e1e9-4eaa-a089-7aa02e55e46b
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Jackson, Paul B.
8c57df38-6cb2-488d-afec-b154d3ddf1cc
Johnson, Taylor T.
204159bb-e1e9-4eaa-a089-7aa02e55e46b

Sogokon, Andrew, Jackson, Paul B. and Johnson, Taylor T. (2019) Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants. Journal of Automated Reasoning, 63 (4), 1005-1029. (doi:10.1007/s10817-018-9497-x).

Record type: Article

Abstract

We describe a method for verifying the temporal property of persistence in non-linear hybrid systems. Given some system and an initial set of states, the method establishes 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 flowpipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study 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 flowpipes or just reasoning about invariants alone can be insufficient and shows the richness of systems that one can handle with the proposed method, since the systems features modes with non-polynomial ODEs. We also propose an alternative method for proving persistence that relies solely on flowpipe computation.

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Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants - Accepted Manuscript
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Accepted/In Press date: 16 November 2018
e-pub ahead of print date: 24 November 2018
Published date: 1 December 2019

Identifiers

Local EPrints ID: 439288
URI: http://eprints.soton.ac.uk/id/eprint/439288
ISSN: 0168-7433
PURE UUID: 7a21ce16-d211-4f25-838e-345aead14eeb

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Date deposited: 07 Apr 2020 16:37
Last modified: 06 Oct 2020 17:55

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