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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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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Abstract 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.
AbstractList 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.
Author Imura, J.
Ishizaki, T.
Girard, A.
Aihara, K.
Luonan Chen
Kashima, K.
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  surname: Ishizaki
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  givenname: K.
  surname: Kashima
  fullname: Kashima, K.
  email: kashima@sys.es.osaka-u.ac.jp
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  givenname: A.
  surname: Girard
  fullname: Girard, A.
  email: Antoine.Girard@imag.fr
  organization: Lab. Jean Kuntzmann, Univ. of Grenoble, Grenoble, France
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  givenname: J.
  surname: Imura
  fullname: Imura, J.
  email: imura@mei.titech.ac.jp
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  surname: Luonan Chen
  fullname: Luonan Chen
  email: lnchen@sibs.ac.cn
  organization: Chinese Acad. of Sci., China
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  givenname: K.
  surname: Aihara
  fullname: Aihara, K.
  email: aihara@sat.t.u-tokyo.ac.jp
  organization: Inst. of Ind. Sci., Univ. of Tokyo, Tokyo, Japan
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Snippet 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...
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StartPage 4175
SubjectTerms Chemicals
Eigenvalues and eigenfunctions
Equations
Manganese
Mathematical model
Redundancy
Vectors
Title Clustering-based ℌ2-state aggregation of positive networks and its application to reduction of chemical master equations
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