Clustering-based ℌ2-state aggregation of positive networks and its application to reduction of chemical master equations

In this paper, based on a notion of network clustering, we propose a state aggregation method for positive systems evolving over directed networks, which we call positive networks. In the proposed method, we construct a set of clusters (i.e., disjoint sets of state variables) according to a kind of...

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Bibliographic Details
Published in:2012 IEEE 51st IEEE Conference on Decision and Control (CDC) pp. 4175 - 4180
Main Authors: Ishizaki, T., Kashima, K., Girard, A., Imura, J., Luonan Chen, Aihara, K.
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2012
Subjects:
Chemicals
Eigenvalues and eigenfunctions
Equations
Manganese
Mathematical model
Redundancy
Vectors
ISBN:9781467320658, 146732065X
ISSN:0191-2216
Online Access:Get full text
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Summary:In this paper, based on a notion of network clustering, we propose a state aggregation method for positive systems evolving over directed networks, which we call positive networks. In the proposed method, we construct a set of clusters (i.e., disjoint sets of state variables) according to a kind of local uncontrollability of systems. This method preserves interconnection topology among clusters as well as stability and some particular properties, such as system positivity and steady-state characteristic (steady-state distribution). In addition, we derive an ℌ 2 -error bound of the state discrepancy caused by the aggregation. The efficiency of the proposed method is shown through the reduction of a chemical master equation representing the time evolution of the Michaelis-Menten chemical reaction system.
ISBN:9781467320658
146732065X
ISSN:0191-2216
DOI:10.1109/CDC.2012.6426793