Clustered model reduction of positive directed networks

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...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 59; pp. 238 - 247
Main Authors: Ishizaki, Takayuki, Kashima, Kenji, Girard, Antoine, Imura, Jun-ichi, Chen, Luonan, Aihara, Kazuyuki
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2015
Elsevier
Subjects:
Automatic
Chemical master equations
Computer Science
Engineering Sciences
Mathematics
Model reduction
Network clustering
Optimization and Control
Positive linear systems
Systems and Control
Network clustering
Model reduction
Chemical master equations
Positive linear systems
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2015.06.027