Clustered model reduction of positive directed networks
Clustered model reduction of positive directed networks
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DOI：
10.1016/j.automatica.2015.06.027
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
T. Ishizaki;K. Kashima;A. Girard;J. Imura;Luonan Chen;K. Aihara
中科院分区：
文献类型：
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作者：
T. Ishizaki;K. Kashima;A. Girard;J. Imura;Luonan Chen;K. Aihara
针对有向网络上演化的半稳定正线性系统，提出了一种聚类模型降阶方法。在这种方法中，我们构建了一组集群，即不相交的状态变量集，基于集群约简的概念，定义为局部状态的不可控性。通过聚集与Frobenius特征向量相关联的聚集系数的可约集群，我们得到一个近似模型，保留集群之间的网络结构，但也有几个基本属性，如半稳定性，积极性，和稳态特性。此外，它被发现，集群约简可以其特征在于半稳定系统的基础上的投影可控Gramian，导致一个先验的H2误差界的状态差异所造成的聚集。所提出的方法的效率证明通过一个说明性的例子，酶催化反应系统所描述的化学主方程。这捕获的化学反应系统的时间演化方面的一组常微分方程。
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, ie, 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 H 2-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.