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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| Published in: | Automatica (Oxford) Vol. 59; pp. 238 - 247 |
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01.09.2015
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Ishizaki, Takayuki Kashima, Kenji Imura, Jun-ichi Aihara, Kazuyuki Girard, Antoine Chen, Luonan |
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| Cites_doi | 10.1016/j.physrep.2005.10.009 10.1137/060666457 10.1016/0024-3795(92)90031-5 10.1016/j.automatica.2011.02.032 10.1109/TAC.2007.911361 10.1137/060666123 10.1109/TAC.1982.1102855 10.1016/j.automatica.2007.05.007 10.1080/03081087808817203 10.1023/A:1022205420182 10.1109/TAC.2013.2275891 |
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| Keywords | Network clustering Model reduction Chemical master equations Positive linear systems |
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| SubjectTerms | Automatic Chemical master equations Computer Science Engineering Sciences Mathematics Model reduction Network clustering Optimization and Control Positive linear systems Systems and Control |
| Title | Clustered model reduction of positive directed networks |
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