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“Abstraction of Dynamical Systems by Timed Automata”

Authors: Rafael Wisniewski and Christoffer Sloth,
Affiliation: Aalborg University
Reference: 2011, Vol 32, No 2, pp. 79-90.

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Keywords: verification, stability, abstraction, timed automata

Abstract: To enable formal verification of a dynamical system, given by a set of differential equations, it is abstracted by a finite state model. This allows for application of methods for model checking. Consequently, it opens the possibility of carrying out the verification of reachability and timing requirements, which by classical control methods is impossible. We put forward a method for abstracting dynamical systems, where level sets of Lyapunov functions are used to generate the partitioning of the state space. We propose to partition the state space using an entire family of functions. The properties of these functions ensure that the discrete model captures the behaviors of a dynamical system by generating appropriate equivalence classes of the states. These equivalence classes make up the partition of the state space.

PDF PDF (483 Kb)        DOI: 10.4173/mic.2011.2.3

DOI forward links to this article:
  [1] Christoffer Sloth and Rafael Wisniewski (2013), doi:10.1016/j.nahs.2012.05.003
  [2] Christoffer Sloth and Rafael Wisniewski (2012), doi:10.3182/20120829-3-IT-4022.00049
  [3] Stefano Schivo and Rom Langerak (2017), doi:10.1007/978-3-319-68270-9_15
  [4] Nikola Bene , Lubo Brim, Jana Dra anovŠ, Samuel Pastva and David afrŠnek (2019), doi:10.1145/3302504.3311793

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  title={{Abstraction of Dynamical Systems by Timed Automata}},
  author={Wisniewski, Rafael and Sloth, Christoffer},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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