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

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 quant...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 57; H. 9; S. 2235 - 2249
Hauptverfasser: Bamieh, B., Jovanovic, M. R., Mitra, P., Patterson, S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.09.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Applied sciences
Asymptotic properties
Coherence
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Computer systems performance. Reliability
Control systems
Control theory
Control theory. Systems
Convolution
Dimensional measurements
Disturbances
Exact sciences and technology
Feedback
Ground, air and sea transportation, marine construction
Heuristic algorithms
Measurement uncertainty
Networks
Road transportation and traffic
Robotics
Software
Studies
Vehicle dynamics
Vehicles
Vehicular formation
Energetics
Performance evaluation
Motor car
Large dimension
Vehicular formation
Scale effect
Automated highways
Feedback regulation
Bullwhip effect
Distributed system
Consensus
Lattice
Network topology
Coherence
Size effect
Complex network
Vehicle platoon
Asymptotic approximation
Large scale
Formation
ISSN:0018-9286, 1558-2523
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Beschreibung
Zusammenfassung: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2202052