Structure-based Clustering Algorithm for Model Reduction of Large-scale Network Systems

Abstract

A model reduction technique is presented that identifies and aggregates clusters in a large-scale network system and yields a reduced model with tractable dimension. The network clustering problem is translated to a graph reduction problem, which is formulated as a minimization of distance from lumpability. The problem is a non-convex, mixedinteger optimization problem and only depends on the graph structure of the system. We provide a heuristic algorithm to identify clusters that are not only suboptimal but are also connected, that is, each cluster forms a connected induced subgraph in the network system.

Boundary Control for Stabilization of Large-Scale Networks through the Continuation Method

“…However, the system still oscillates. The oscillations can be suppressed by applying control (7) with kernel (6), where we took c = 10. Successful suppression is depicted in Fig.…”

“…Mostly, the methods of network analysis "forget" information about positions, relying only on interaction topology. Among examples of methods of this type, there is model reduction, in particular clustering of the original network depending on the topology [5], [6] or reduction towards the average state [7], [8].…”

11 Reduced-order modeling of large-scale network systems

“…An iterative approach for single-integrator networks can be found in [11], and an alternative clustering method is presented in [63], which takes into account the connectedness of vertices such that the vertices in each cluster form a connected graph.…”

“…The works in [11,13] extend the notion of dissimilarity for dynamical systems, where nodal behaviors are represented by the transfer functions mapping from external inputs to node states, and dissimilarity between two nodes are quantified by the norm of their behavior deviation. Then clustering algorithms, e. g., hierarchical clustering and K-means clustering, can be adapted to group nodes in such a way that nodes in the same cluster are more similar to each other than to those in other clusters [12,63]. Subsequent research in [12,22,17,19] shows that the dissimilarity-based clustering method can also be extended to second-order networks, controlled power networks, and directed networks.…”

Average State Estimation in Large-Scale Clustered Network Systems

“…Graph theoretically, this condition of A-invariance is satisfied only if the clusters of a network system are chosen according to an (almost) equitable partition, [12]- [16]. However, achieving exact lumpability by network partitioning is quite difficult, as remarked in [17]. This is due to the constraints on sensor locations and number of clusters, and, in physical network systems, the clusters are also required to be connected, [18].…”