Model Reduction of Complex Dynamical Networks based on State Aggregation

English

Séminaire Modèles et Algorithmes Déterministes: CASYS

3/11/2011 - 09:45 Mr Takayuki Ishizaki (Tokyo Institute of Technology) Salle 1 - Tour IRMA

In this talk, I present a network structure preserving model reduction method for a linear system evolving on large-scale complex networks. In this method, we construct a set of clusters (i.e., disjoint subsets of state variables) based on a kind of local controllability of the state-space, which can be determined through two kinds of indices: one is based on a basis expansion implemented as matrix tri-diagonalization, and the other is based on the controllability gramian. Aggregating the constructed clusters, we obtain a reduced model that preserves interconnection topology of the clusters as well as some particular properties, such as stability, steady-state characteristic and system positivity. In addition, an H_{?infty}/H2-error bound of the state discrepancy caused by the aggregation is derived. The efficiency of the proposed method is shown by a numerical example including a large-scale complex network.