On the Coherence of Large-Scale Networks With Distributed PI and PD Control

Tegling, Emma

doi:10.1109/lcsys.2017.2711781

Cited by 26 publications

(20 citation statements)

References 16 publications

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“…An intuitive explanation to this result, which was also established in [24], is that the dynamic feedback protocol serves as a distributed integral controller, which integrates absolute measurements of velocities in time to yield a substitute for absolute position data. With absolute data from both position and velocity, formations are known to be fully coherent [1].…”

Section: B Performance Improvement With Distributed Integral Controlmentioning

confidence: 68%

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

Tegling

Mitra

Bamieh

2019

IEEE Trans. Automat. Contr.

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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 1-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 accordion-like 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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Section: B Performance Improvement With Distributed Integral Controlmentioning

confidence: 68%

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

Tegling

Mitra

Bamieh

2019

IEEE Trans. Automat. Contr.

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“…The attacker can obtain these values by deploying additional sensors, but can also get this information for free. Namely, control algorithms sometimes base decision on the neighboring and local state to achieve better performance [41]. Hence, if the attacker remains undetected, nodes may continue sending the state information to the compromised actuators, not knowing that these actuators are controlled by the attacker.…”

Section: Relation Of δ R To Different Types Of Attackersmentioning

confidence: 99%

Actuator Security Indices Based on Perfect Undetectability: Computation, Robustness, and Sensor Placement

Milošević

Teixeira

Johansson

2020

IEEE Trans. Automat. Contr.

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This paper proposes an actuator security index based on the definition of perfect undetectability. This index can help a control system operator to localize the most vulnerable actuators in a networked control system, which can then be secured. Particularly, the security index of an actuator equals the minimum number of sensors and actuators that needs to be compromised, such that a perfectly undetectable attack against that actuator can be conducted. A method for computing the index for small scale networked control systems is derived, and it is shown that the index can potentially be increased by placing additional sensors. The difficulties that appear once the system is of a large scale are then outlined: the problem of calculating the index is NP-hard, the index is vulnerable to system variations, and it is based on the assumption that the attacker knows the entire model of the system. To overcome these difficulties, a robust security index is introduced. The robust index can be calculated in polynomial time, it is unaffected by the system variations, and it can be related to both limited and full model knowledge attackers. Additionally, we analyze two sensor placement problems with the objective to increase the robust indices. We show that both of these problems have submodular structures, so their suboptimal solutions with performance guarantees can be obtained in polynomial time. Finally, the theoretical developments are illustrated through numerical examples.

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“…This means that the system can never have bounded variance in terms of the global error measurement (8). However, a bounded variance and thus scalability in terms of the local error (9) can be achieved by a re-tuning of the controller.…”

Section: From Distributed To Centralized Integral Controlmentioning

confidence: 99%

Noise-induced limitations to the scalability of distributed integral control

Tegling

2019

Systems & Control Letters

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We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H 2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise's impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this may in practice imply that very large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.

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On the Coherence of Large-Scale Networks With Distributed PI and PD Control

Cited by 26 publications

References 16 publications

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

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

Actuator Security Indices Based on Perfect Undetectability: Computation, Robustness, and Sensor Placement

Noise-induced limitations to the scalability of distributed integral control

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