Projection-Based Model Reduction of Multi-Agent Systems Using Graph Partitions

Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds

“…2. We extend the results in [26] for single integrator dynamics by giving an explicit expression for the H ∞ model reduction error in terms of properties of the given graph partition. 3.…”

“…Following [26], the idea to obtain such an approximation is to cluster groups of agents in the network, and to treat each of the resulting clusters as a node in a new, reduced order, network. The reduced order network will again be a leader-follower network, and by the clustering procedure, essential interconnection features of the network will be preserved.…”

“…Extending the main idea in [26], we take as reduced order system the Petrov-Galerkin projection of the original system (4), with the following choice for the matrices V and W :…”

“…In [26], model reduction by clustering was put in the context of model order reduction by Petrov-Galerkin projection. The results in [26] provide explicit expressions for the H 2 model reduction error if a leader-follower network with single integrator agent dynamics is clustered using an almost equitable partition of the graph.…”

“…The results in [26] provide explicit expressions for the H 2 model reduction error if a leader-follower network with single integrator agent dynamics is clustered using an almost equitable partition of the graph. In the present paper, our aim is to generalize and extend the results in [26] to networks where the agent dynamics is given by an arbitrary multivariable input-state-output system. We also aim at finding explicit formulas and a priori upper bounds for the model reduction error measured in the H ∞ -norm.…”