We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge capacities are small compared to the dimensionality of the state vectors, it is not possible to instantaneously communicate full state information over every edge. We investigate how robust consensus (small steady state variance of the states) can be achieved within a linear time-invariant setting by optimally assigning edges to state-dimensions. We show that a finite steady state variance of the states can be achieved if and only if the minimum cut capacity of the network is not smaller than the dimensionality of the state vectors. Optimal and approximate solutions are provided for some special classes of graphs. We also consider the related problem of optimally allocating additional capacity on a feasible initial solution. We show that this problem corresponds to the maximization of a submodular function subject to a matroid constraint, which can be approximated via a greedy algorithm.
|Original language||English (US)|
|Title of host publication||2021 American Control Conference, ACC 2021|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - May 25 2021|
|Event||2021 American Control Conference, ACC 2021 - Virtual, New Orleans, United States|
Duration: May 25 2021 → May 28 2021
|Name||2021 American Control Conference (ACC)|
|Conference||2021 American Control Conference, ACC 2021|
|City||Virtual, New Orleans|
|Period||5/25/21 → 5/28/21|
Bibliographical notePublisher Copyright:
© 2021 American Automatic Control Council.