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Clustered model reduction of positive directed networks

Authors :
Kazuyuki Aihara
Takayuki Ishizaki
Jun-ichi Imura
Luonan Chen
Antoine Girard
Kenji Kashima
Tokyo Institute of Technology [Tokyo] (TITECH)
Graduate School of Information Science and Technology [Osaka]
Osaka University [Osaka]
Calculs Algébriques et Systèmes Dynamiques (CASYS)
Laboratoire Jean Kuntzmann (LJK)
Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)
Laboratoire de Recherche en Informatique (LRI)
Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Institute of Industrial Science (IIS)
The University of Tokyo (UTokyo)
Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
The University of Tokyo
Source :
Automatica, Automatica, Elsevier, 2015, 59, pp.238-247. ⟨10.1016/j.automatica.2015.06.027⟩
Publication Year :
2015
Publisher :
Elsevier BV, 2015.

Abstract

International audience; This paper proposes a clustered model reduction method for semistable positive linear systems evolving over directed networks. In this method, we construct a set of clusters, i.e., disjoint sets of state variables, based on a notion of cluster reducibility, defined as the uncontrollability of local states. By aggregating the reducible clusters with aggregation coefficients associated with the Frobenius eigenvector, we obtain an approximate model that preserves not only a network structure among clusters, but also several fundamental properties, such as semistability, positivity, and steady state characteristics. Furthermore, it is found that the cluster reducibility can be characterized for semistable systems based on a projected controllability Gramian that leads to an a priori H2-error bound of the state discrepancy caused by aggregation. The efficiency of the proposed method is demonstrated through an illustrative example of enzyme-catalyzed reaction systems described by a chemical master equation. This captures the time evolution of chemical reaction systems in terms of a set of ordinary differential equations.

Details

ISSN :
00051098
Volume :
59
Database :
OpenAIRE
Journal :
Automatica
Accession number :
edsair.doi.dedup.....711a003f1a528b9b420a6ae4b472337b
Full Text :
https://doi.org/10.1016/j.automatica.2015.06.027