Clustering-Based H2-State Aggregation of Positive Networks and Its Application to Reduction of Chemical Master Equations

Abstract : In this paper, we propose a state aggregation method for positive systems evolving on directed networks, which we call positive networks, based on a notion of network clustering. Furthermore, we apply the proposed method to the reduction of chemical master equations. In this method, we construct a set of clusters (i.e., disjoint subsets of state variables) according to local uncontrollability of systems. The aggregation of the constructed clusters under suitable weights provides a reduced model that preserves the interconnection topology among clusters as well as the stability and some particular properties, such as system positivity and steady-state characteristic (steady-state distribution). In addition, we derive an H2-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.
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https://hal.archives-ouvertes.fr/hal-00769676
Contributor : Brigitte Bidégaray-Fesquet <>
Submitted on : Thursday, January 3, 2013 - 12:17:16 AM
Last modification on : Thursday, July 4, 2019 - 9:54:02 AM

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Takayuki Ishizaki, Kenji Kashima, Antoine Girard, Jun-Ichi Imura, Luonan Chen, et al.. Clustering-Based H2-State Aggregation of Positive Networks and Its Application to Reduction of Chemical Master Equations. CDC 2012 - 51st IEEE Conference on Decision and Control, Dec 2012, Maui, Hawaii, United States. pp.4175-4180, ⟨10.1109/CDC.2012.6426793⟩. ⟨hal-00769676⟩

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