In this talk we establish a projection based model reduction method for multi-agent systems defined on a graph. Reduced order models are obtained by clustering the vertices (agents) of the underlying communication graph by means of suitable graph partitions. In the reduction process the spatial structure of the network is preserved and the reduced order models can again be realized as multi-agent systems defined on a graph. The agents are assumed to have single-integrator dynamics and the communication graph of the original system is weighted and undirected. The proposed model reduction technique reduces the number of vertices of the graph (which is equal to the dynamic order of the original multi-agent system) and yields a reduced order multi-agent system defined on a new graph with a reduced number of vertices. This new graph is a weighted symmetric directed graph. It is shown that if the original multi-agent system reaches consensus, then so does the reduced order model. For the case that the clusters are chosen using an almost equitable partition of the graph, we obtain an explicit formula for the H-2 norm of the error system obtained by comparing the input-output behaviors of the original model and the reduced order model. We also obtain an upper bound for the H-infinity norm of the error system. Finally, we generalize the results to multi-agent system with arbitrary agent dynamics.

Harry L. Trentelman is a full professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science of the University of Groningen, the Netherlands. From 1985 to 1991 he served as an assistant professor, and as an associate professor at the Mathematics Department of the Eindhoven University of Technology, the Netherlands. He is a member of the Jan C. Willems Center for Systems and Control. He held visiting and research positions at University of Kyoto and Australian National University. He serves as a senior editor of the IEEE Transactions on Automatic Control. He is past associate editor of Automatica, SIAM Journal on Control and Optimization, and Systems and Control Letters. Dr. Trentelman is a Fellow of the IEEE.