Algorithmic Approach to Abstracting Linear Systems by Timed Automata

Christoffer Sloth, Rafael Wisniewski

Research output: Contribution to journalConference article in JournalResearchpeer-review

1 Citation (Scopus)
285 Downloads (Pure)

Abstract

This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems.

The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction.

The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions.
The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools.
Original languageEnglish
Book seriesI F A C Workshop Series
Pages (from-to)4546-4551
Number of pages6
ISSN1474-6670
DOIs
Publication statusPublished - 2011
Event18th IFAC World Congress - Milano, Italy
Duration: 28 Aug 20112 Sep 2011

Conference

Conference18th IFAC World Congress
CountryItaly
CityMilano
Period28/08/201102/09/2011

Fingerprint

Lyapunov functions
Linear systems
Dynamical systems
Trajectories

Cite this

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title = "Algorithmic Approach to Abstracting Linear Systems by Timed Automata",
abstract = "This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions. The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools.",
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Algorithmic Approach to Abstracting Linear Systems by Timed Automata. / Sloth, Christoffer; Wisniewski, Rafael.

In: I F A C Workshop Series, 2011, p. 4546-4551.

Research output: Contribution to journalConference article in JournalResearchpeer-review

TY - GEN

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AU - Sloth, Christoffer

AU - Wisniewski, Rafael

PY - 2011

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AB - This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions. The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools.

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