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On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

Tegling, Emma LU ; Mitra, Partha ; Sandberg, Henrik LU and Bamieh, Bassam (2019) In IEEE Transactions on Automatic Control 64(12). p.4936-4951
Abstract

In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing,... (More)

In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20-200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.

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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Networked control systems
in
IEEE Transactions on Automatic Control
volume
64
issue
12
article number
8684336
pages
16 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85068842657
ISSN
0018-9286
DOI
10.1109/TAC.2019.2909811
language
English
LU publication?
no
additional info
Publisher Copyright: © 1963-2012 IEEE.
id
353ad519-1dfc-486e-bbb6-7237d6174a48
date added to LUP
2021-11-24 09:51:29
date last changed
2022-04-27 06:05:43
@article{353ad519-1dfc-486e-bbb6-7237d6174a48,
  abstract     = {{<p>In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20-200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.</p>}},
  author       = {{Tegling, Emma and Mitra, Partha and Sandberg, Henrik and Bamieh, Bassam}},
  issn         = {{0018-9286}},
  keywords     = {{Networked control systems}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{4936--4951}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks}},
  url          = {{http://dx.doi.org/10.1109/TAC.2019.2909811}},
  doi          = {{10.1109/TAC.2019.2909811}},
  volume       = {{64}},
  year         = {{2019}},
}