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We investigate the performance of linear consensus algorithms subject to a scaling of the underlying network size. Specifically, we model networked systems with nth order integrator dynamics over families of undirected, weighted graphs with bounded nodal degrees. In such networks, the algebraic connectivity affects convergence rates, sensitivity, and, for high-order consensus [n ≥ 3), stability properties. This connectivity scales unfavorably in network size, except in expander families, where consensus performs well regardless of network size. We show, however, that consensus over expander families is fragile to a grounding of the network (resulting in leader-follower consensus). We show that grounding may deteriorate system performance by orders of magnitude in large networks, or cause instability in high-order consensus. Our results, which we illustrate through simulations, also point to a fundamental limitation to the scalability of consensus networks with leaders, which does not apply to leaderless networks.
|Title of host publication||8th IFAC Workshop on Distributed Estimation and Control in Networked Systems|
|Number of pages||6|
|Publication status||Published - 2019|
|Event||8th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NECSYS 2019 - Chicago, United States|
Duration: 2019 Sep 16 → 2019 Sep 17
|Conference||8th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NECSYS 2019|
|Period||2019/09/16 → 2019/09/17|
Bibliographical notePublisher Copyright:
© 2019 IFAC-PapersOnLine. All rights reseved.
Subject classification (UKÄ)
- Control Engineering
- Distributed control
- Large-scale systems
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