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