Petar Mlinarić

Efficient model order reduction for multi-agent systems using QR decomposition-based clustering

In this paper we present an efficient model order reduction method for multi-agent systems with Laplacian-based dynamics. The method combines an established model order reduction method and a clustering algorithm to produce a graph partition used for reduction, thus preserving structure and consensus. By the Iterative Rational Krylov Algorithm, a good reduced order model can be found which is not necessarily structure preserving. However, based on this we can efficiently find a partition using the QR decomposition with column pivoting as a clustering algorithm, so that the structure can be restored. We illustrate the effectiveness on an example from the open literature.

Model reduction of linear multi-agent systems by clustering with \(\varvec{\mathcal {H}_2}\) and \(\varvec{\mathcal {H}_\infty }\) error bounds

In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst 1(2):145–154, 2014. https://doi.org/10.1109/TCNS.2014.2311883), model reduction of leader–follower multi-agent networks by clustering was studied. For such multiagent networks, a reduced order network is obtained by partitioning the set of nodes in the graph into disjoint sets, called clusters, and associating with each cluster a single, new, node in a reduced network graph. In Monshizadeh et al. (2014), this method was studied for the special case that the agents have single integrator dynamics. For a special class of graph partitions, called almost equitable partitions, an explicit formula was derived for the H2 model reduction error. In the present paper, we will extend and generalize the results from Monshizadeh et al. (2014) in a number of directions. This research is supported by a research grant of the “International Max Planck Research School (IMPRS) for Advanced Methods in Process and System Engineering (Magdeburg)”. B Petar Mlinarić mlinaric@mpi-magdeburg.mpg.de Hidde-Jan Jongsma h.jongsma@rug.nl Sara Grundel grundel@mpi-magdeburg.mpg.de Peter Benner benner@mpi-magdeburg.mpg.de Harry L. Trentelman h.l.trentelman@rug.nl 1 Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands 2 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany