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Discrete Abstraction of Multiaffine Systems

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2016

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Kong, Hui
Bartocci, Ezio
Bogomolov, Sergiy
Grosu, Radu
Henzinger, Thomas A.
Jiang, Yu

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https://doi.org/10.1007/978-3-319-47151-8_9
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CINQUEMANI, Eugenio, ed., Alexandre DONZÉ, ed.. Hybrid Systems Biology. Cham: Springer, 2016, pp. 128-144. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-47150-1. Available under: doi: 10.1007/978-3-319-47151-8_9

Zusammenfassung

Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction significantly determines the level of confidence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sufficient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiaffine system to be based on a set of multivariate polynomials. Hence, a rectangular partition defined in terms of polynomials of the form (xi−c) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.

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004 Informatik

Schlagwörter

Multiaffine system, Hybrid system, Discrete abstraction, State space partition, Gröbner basis

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HSB: International Workshop on Hybrid Systems Biology, 5th International Workshop, HSB 2016, 20. Okt. 2016 - 21. Okt. 2016, Grenoble
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ISO 690KONG, Hui, Ezio BARTOCCI, Sergiy BOGOMOLOV, Radu GROSU, Thomas A. HENZINGER, Yu JIANG, Christian SCHILLING, 2016. Discrete Abstraction of Multiaffine Systems. HSB: International Workshop on Hybrid Systems Biology, 5th International Workshop, HSB 2016. Grenoble, 20. Okt. 2016 - 21. Okt. 2016. In: CINQUEMANI, Eugenio, ed., Alexandre DONZÉ, ed.. Hybrid Systems Biology. Cham: Springer, 2016, pp. 128-144. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-47150-1. Available under: doi: 10.1007/978-3-319-47151-8_9
BibTex
@inproceedings{Kong2016Discr-53641,
  year={2016},
  doi={10.1007/978-3-319-47151-8_9},
  title={Discrete Abstraction of Multiaffine Systems},
  isbn={978-3-319-47150-1},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  booktitle={Hybrid Systems Biology},
  pages={128--144},
  editor={Cinquemani, Eugenio and Donzé, Alexandre},
  author={Kong, Hui and Bartocci, Ezio and Bogomolov, Sergiy and Grosu, Radu and Henzinger, Thomas A. and Jiang, Yu and Schilling, Christian}
}
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