Edge-matching graph contractions and their interlacing properties

Leiter, Noam; Zelazo, Daniel

doi:10.1016/j.laa.2020.11.003

Cited by 1 publication

(2 citation statements)

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“…Given a graph G = (V, E), and an n − r edge subset E S ⊆ E, an edge-induced partition π(E S ) is an r-partition of V constructed as follows [19]: (i) A graph G(V, E S ) is created from the vertices of G and the edge-subset E S , (ii) the connected components of G(V, E S ) are found, (iii) the vertices of each component is registered as a partition cell, and the set of all components cells constitutes the partition π(E S ) of V (Figure 5).…”

Section: Model Reduction Of Multi-agent Systems By Graph Contractionsmentioning

confidence: 99%

“…We then demonstrate the tree-based IIPROM bound algorithm (Algorithm 2) on the LCC. The spanning tree edges are found and Algorithm 2 is then performed for r ∈ [10,19]. has a quasi-linear trend as a function of n−r n , and that the bound is tight for low reduction depths and differs as the reduction increases; however, the bound follows the same trend as the error, therefore, minimizing the bound is consistent with minimizing the error in this case.…”

Section: A Iiprom Of a Small-scale Lapalcian Consensus Modelmentioning

confidence: 99%

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Product Form of Projection-Based Model Reduction and its Application to Multi-Agent Systems

Leiter¹,

Zelazo²

2021

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Orthogonal projection-based reduced order models (PROM) are the output of widely-used model reduction methods. In this work, a novel product form is derived for the reduction error system of these reduced models, and it is shown that any such PROM can be obtained from a sequence of 1-dimensional projection reductions. Investigating the error system product form, we then define interface-invariant PROMs, model order reductions with projection-invariant input and output matrices, and it is shown that for such PROMs the error product systems are strictly proper. Furthermore, exploiting this structure, an analytic H∞ reduction error bound is obtained and an H∞ bound optimization problem is defined. Interface-invariant reduced models are natural to graph-based model reduction of multi-agent systems where subsets of agents function as the input and output of the system. In the second part of this study, graph contractions are used as a constructive solution approach to the H∞ bound optimization problem for multi-agent systems. Edgebased contractions are then utilized in a greedy-edge reduction algorithm and are demonstrated for the model reduction of a first-order Laplacian controlled consensus protocol.

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Section: Model Reduction Of Multi-agent Systems By Graph Contractionsmentioning

confidence: 99%

Section: A Iiprom Of a Small-scale Lapalcian Consensus Modelmentioning

confidence: 99%