Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

By Bassam Bamieh, M. Jovanovi'c, Partha P. Mitra, S. Patterson. IEEE Transactions on Automatic Control, 2011

437 citations recorded by the source corpus.

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2, and higher dimensions, with vehicular platoons corresponding to the 1-D case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent 1-D vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Subfields: Biomedical Engineering, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2784dcfdc3fc5726bc2426692dbad06a5b3338ce

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. M. Jovanovi'c
2. Florian Dörfler

In Computer Networks and Communications

1. J. Karl Hedrick
2. M. Jovanovi'c
3. Yang Zheng
4. Keqiang Li
5. Shengbo Eben Li
6. Florian Dörfler
7. Francesco Bullo

In Control and Systems Engineering

1. Florian Dörfler
2. Xiaofan Wu
3. Shengbo Eben Li
4. Keqiang Li
5. M. Jovanovi'c
6. Yang Zheng
7. J. Karl Hedrick
8. Makan Fardad

Citations in the corpus

• Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers (2011, background): “Following [36], we consider the local and global performance errors that render the average mode x̄ unobservable.”
• Dynamical Modeling and Distributed Control of Connected and Automated Vehicles: Challenges and Opportunities (2017, background): “This captures the notion of coherence [40], [54].”
• Input-Output Analysis and Decentralized Optimal Control of Inter-Area Oscillations in Power Systems (2015, methodology): “A similar approach was recently employed to quantify performance of consensus and synchronization networks [19], [20].”