Model reduction of networked passive systems through clustering

In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a reduced-order networked system that allows for a convenient physical interpretation. The identification of the subsystems to be clustered is performed through controllability and observability analysis of an associated edge system and it is shown that the property of synchronization (i.e., the convergence of trajectories of the subsystems to each other) is preserved during reduction. The results are illustrated by means of an example.Comment: 7 pages, 2 figures; minor changes in the final version, as accepted for publication at the 13th European Control Conference, Strasbourg, Franc

Balanced Truncation of Networked Linear Passive Systems

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example

The price of connectedness in graph partitioning problems

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Stability and synchronization preserving model reduction of multi-agent systems

In this paper, stability and synchronization preserving model reduction schemes are developed for linear multi-agent systems. The multi-agent systems that are considered here are composed of general, yet identical linear subsystems, and the communication topology is assumed to be time-independent. First, under the assumption that the agents have stable internal dynamics and the network is stable, the dynamic order of the agents is reduced such that the corresponding reduced order network is again stable. Then, starting from a synchronized network where agents are allowed to have unstable dynamics, a reduced order model for the network which preserves synchronization is obtained. In addition, model reduction error bounds are established to compare the behavior of the original network to that of the reduced order model. The proposed results are illustrated through a numerical example. © 2012 Elsevier B.V. All rights reserved

Stability and synchronization preserving model reduction of multi-agent systems

In this paper, stability and synchronization preserving model reduction schemes are developed for linear multi-agent systems. The multi-agent systems that are considered here are composed of general, yet identical linear subsystems, and the communication topology is assumed to be time-independent. First, under the assumption that the agents have stable internal dynamics and the network is stable, the dynamic order of the agents is reduced such that the corresponding reduced order network is again stable. Then, starting from a synchronized network where agents are allowed to have unstable dynamics, a reduced order model for the network which preserves synchronization is obtained. In addition, model reduction error bounds are established to compare the behavior of the original network to that of the reduced order model. The proposed results are illustrated through a numerical example.