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

Tegling, E., Mitra, P., Sandberg, H., Bamieh, B. (December 2019) On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks. Ieee Transactions on Automatic Control, 64 (12). pp. 4936-4951. ISSN 0018-9286

URL: https://ieeexplore.ieee.org/document/8684336
DOI: 10.1109/tac.2019.2909811


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.

Item Type: Paper
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: Adrian Gomez
Date: December 2019
Date Deposited: 15 Jan 2020 14:50
Last Modified: 15 Jan 2020 14:50
Related URLs:
URI: https://repository.cshl.edu/id/eprint/38902

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