Completeness of Lyapunov Abstraction

Rafal Wisniewski, Christoffer Sloth

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

1 Citation (Scopus)

Abstract

This paper addresses the generation of complete abstractions of polynomial dynamical systems by timed automata. For the proposed abstraction, the state space is divided into cells by sublevel sets of functions. We identify a relation between these functions and their directional derivatives along the vector field, which allows the generation of a complete abstraction.

To compute the functions that define the subdivision of the state space in an algorithm, we formulate a sum of squares optimization problem. This optimization problem finds the best subdivisioning functions, with respect to the ability to approximate the dynamical system, in a subset of admissible subdivisioning functions.
Original languageEnglish
Title of host publication Proceedings Third International Workshop on Hybrid Autonomous Systems (HAS 2013)
EditorsLuca Bortolussi, Manuela L. Bujorianu, Giordano Pola
Number of pages17
PublisherOpen Publishing Association
Publication date2013
Pages26-42
DOIs
Publication statusPublished - 2013
EventThird International Workshop on Hybrid Autonomous Systems - Rome, Italy
Duration: 17 Mar 2013 → …

Conference

ConferenceThird International Workshop on Hybrid Autonomous Systems
Country/TerritoryItaly
CityRome
Period17/03/2013 → …
SeriesElectronic Proceedings in Theoretical Computer Science
Volume124
ISSN2075-2180

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