Clustered model reduction of interconnected second-order systems

  • Ishizaki Takayuki
    Graduate School of Information Science and Engineering, Tokyo Institute of Technology CREST, Japan Science and Technology Agency
  • Imura Jun-ichi
    Graduate School of Information Science and Engineering, Tokyo Institute of Technology CREST, Japan Science and Technology Agency

抄録

In this paper, we propose a clustered model reduction method for interconnected second-order systems evolving over undirected networks, which we call second-order networks. In this model reduction method, network clustering, i.e., clustering of subsystems, is performed according to cluster reducibility, which is defined as a notion of weak controllability of local subsystem states. This paper clarifies that the cluster reducibility can be algebraically characterized for second-order networks through the controller-Hessenberg transformation of their first-order representation. By aggregating the reducible clusters, we obtain an approximate model that preserves an interconnection topology among clustered subsystems. Furthermore, we derive an H-error bound of the state discrepancy caused by the cluster aggregation. Finally, the efficiency of the proposed method is demonstrated through an example of large-scale complex networks.

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