Harry L. Trentelman
Model Reduction of Multi-Agent Systems Using Graph Partitions
Prof. Dr. Harry L. Trentelman
Johann Bernoulli Institute for Mathematics and Computer Science
University of Groningen
The Netherlands
Time & Place
The presentation on April 16, 2015 will be given in the Lukasklause (Schleinufer 1, 39104 Magdeburg) and starts at 5.00 p.m.
Abstract
This talk deals with the problem of model reduction of 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 special 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 prove that the error obtained by taking an arbitrary partition of the graph is bounded from below by the error obtained by using the largest almost equitable partition finer than the given partition. Finally, we extend our results on single integrator dynamics to the case that the agent dynamics is an arbitrary linear input-output system.
Short CV
Harry Trentelman is a full professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science of the University of Groningen. From 1985 to 1991 he served as an assistent professor, and as an associate professor at the Mathematics Department of the University of Technology at Eindhoven, the Netherlands. He obtained his PhD degree in Mathematics from the University of Groningen in 1985. He serves as a senior editor of the IEEE Transactions on Automatic Control and as an associate editor of Automatica. He is past associate editor of the SIAM Journal on Control and Optimization and Systems and Control Letters. Dr. Trentelman is a Fellow of the IEEE.