On aggregate control of clustered consensus networks

Boker, Almuatazbellah M.; Nudell, Thomas R.; Chakrabortty, Aranya

doi:10.1109/acc.2015.7172204

Cited by 20 publications

(17 citation statements)

References 13 publications

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“…The approach summarized next assumes that each node has a single control input; without loss of generality, we set B = I n in (1a). For a more detailed discussion of control inversion we refer the reader to [22].…”

Section: Three-area Case Studymentioning

confidence: 99%

Ensuring localizability of node attacks in consensus networks via feedback graph design

Nudell

Chakrabortty

2015

2015 American Control Conference (ACC)

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In this paper we consider the problem of localizability of attacks in continuous-time consensus networks. In our previous work [1] we showed that if a consensus network is divided into clusters, then a supervisor can successfully localize the cluster in which an attack may have been launched by simply inspecting the sign patterns of the residues corresponding to the slow poles of its input-output transfer function (TF). A necessary condition for localizability, however, was that the attack must enter through a node that guarantees this TF to be minimal. In case the attacker knows the identity of the so-called zero nodes from where the TFs are non-minimal, and chooses to launch the attack at any of them, then the supervisor cannot localize the attack. We show that this problem can be bypassed by designing a state-feedback controller that equivalently changes the algebraic properties of the underlying network graph, and thereby restores minimality of the TF. We illustrate the approach by simulating a three-area, 30-node graph, and highlighting the performance trade-offs that come as a price of localizability.

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Section: Three-area Case Studymentioning

confidence: 99%

Ensuring localizability of node attacks in consensus networks via feedback graph design

Nudell

Chakrabortty

2015

2015 American Control Conference (ACC)

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“…Recall the reduced-order ARE (8). By pre-and postmultiplying it with P T and P , and after a few calculations, we get A TX +XA +Q −XGX = 0, witĥ…”

Section: B Case Ii: Unstable Open-loopmentioning

confidence: 99%

LQG control of large networks: A clustering-based approach

Xue

Chakrabortty

2017

2017 American Control Conference (ACC)

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In this paper we present a set of projection-based designs for constructing simplified linear quadratic regulator (LQR) controllers for large-scale network systems. When such systems have tens of thousands of states, the design of conventional LQR controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithms bypass these difficulties by clustering the system states using structural properties of its closed-loop transfer matrix. The assignment of clusters is defined through a structured projection matrix P , which leads to a significantly lower-dimensional LQR design. The reduced-order controller is finally projected back to the original coordinates via an inverse projection. The problem is, therefore, posed as a model matching problem of finding the optimal set of clusters or P that minimizes the H2-norm of the error between the transfer matrix of the full-order network with the full-order LQR and that with the projected LQR. We derive a tractable relaxation for this model matching problem, and design a P that solves the relaxation. The design is shown to be implementable by a convenient, hierarchical two-layer control architecture, requiring far less number of communication links than full-order LQR.Index Terms-Clustering, Large-scale networks, Projection, LQR, H2 performance.2) Reduced-order LQR design: We similarly project the LQR parameters byQ = P QP T ∈ R r×r , and letR = R such thatG :=BR −1B = P GP T ∈ R r×r . An LQR problem for the reduced-order model (6) is then posed as to minimizẽ J := ∞ 0

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“…More specifically, the dynamics of the local interactions of the nodes within clusters evolve at a faster time scale (due to dense communication) than the slow aggregate dynamics (due to sparse communication) across clusters. This observation has been utilized in a number of works to study the behavior of the popular distributed consensus methods over cluster networks in different applications; see for example [5], [6], [7], [8], [9], [10], [11], [12], [13], [14] and the references therein. We are, however, not aware of any prior works in studying…”

Section: Introductionmentioning

confidence: 99%

Convergence Rates of Decentralized Gradient Methods over Cluster Networks

Dutta¹,

Masrourisaadat²,

Doan³

2021

Preprint

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We present an analysis for the performance of decentralized consensus-based gradient (DCG) methods for solving optimization problems over a cluster network of nodes. This type of network is composed of a number of densely connected clusters with a sparse connection between them. Decentralized algorithms over cluster networks have been observed to constitute two-time-scale dynamics, where information within any cluster is mixed much faster than the one across clusters. Based on this observation, we present a novel analysis to study the convergence of the DCG methods over cluster networks. In particular, we show that these methods converge at a rate ln(T )/T and only scale with the number of clusters, which is relatively small to the size of the network. Our result improves the existing analysis, where these methods are shown to scale with the size of the network. The key technique in our analysis is to consider a novel Lyapunov function that captures the impact of multiple time-scale dynamics on the convergence of this method. We also illustrate our theoretical results by a number of numerical simulations using DCG methods over different cluster networks.

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On aggregate control of clustered consensus networks

Cited by 20 publications

References 13 publications

Ensuring localizability of node attacks in consensus networks via feedback graph design

Ensuring localizability of node attacks in consensus networks via feedback graph design

LQG control of large networks: A clustering-based approach

Convergence Rates of Decentralized Gradient Methods over Cluster Networks

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