Complete Abstractions of Dynamical Systems by Timed Automata

Christoffer Sloth, Rafael Wisniewski

Research output: Contribution to journalJournal articleResearchpeer-review

13 Citations (Scopus)


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
JournalNonlinear Analysis: Hybrid Systems
Issue number1
Pages (from-to)80-100
Publication statusPublished - Feb 2013


  • Abstraction
  • Verification
  • Reachability
  • Timed automata

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