Aggregate control of clustered networks with inter-cluster time delays

Boker, Almuatazbellah M.; Yuan, Chengzhi; Wu, Fen; Chakrabortty, Aranya

doi:10.1109/acc.2016.7526506

Cited by 12 publications

(11 citation statements)

References 11 publications

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“…Distributed consensus methods, a special of DCG, over cluster networks have been observed to constitute two-timescale dynamics, where the information within any cluster is mixed much faster (due to dense communications) than information diffused from one cluster to another (due to sparse communications) [7], [8], [10], [12], [13], [14]. In this paper, we show that this observation continues to hold in the context of DCG method.…”

Section: Problem Formulationsupporting

confidence: 52%

“…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%

“…The key idea in our analysis is to introduce a new composite Lyapunov function with respect to the time-scale separation in the network, inspired by singular perturbation theory [15] and recent analysis for the centralized two-time-scale stochastic approximation [16], [17], [18]. Our approach is different than the typical singular perturbation approach reported in [5], [10], [7] in that it is not based on reducing the system model into two smaller models. This means that our approach does not require the system to be modeled in the standard singular perturbation form, which requires the fast subsystem to have distinct (isolated) real roots.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Problem Formulationsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convergence Rates of Decentralized Gradient Methods over Cluster Networks

Dutta¹,

Masrourisaadat²,

Doan³

2021

Preprint

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“…The first network example shown in Fig. 2 was also considered in [4] and [5]. We apply our upper and lower bounds on the solution to a control problem over a 20 node network with m The results of this network are recorded in Table 1.…”

Section: Examplementioning

confidence: 99%

“…An increasing amount of work [4], [5], [27] has focused on obtaining an approximate solution that is asymptotically equivalent in the singular perturbation parameter δ to the solution of the original problem. In these cases, the parameter δ is chosen to be the clustering parameter of the network that provides the ratio of the number of internal connections to the number of external connections over all areas.…”

Section: Introductionmentioning

confidence: 99%

Error bounds on the solution to an optimal control problem over clustered consensus networks

Howe¹,

Parpas²

2017

2017 Proceedings of the Conference on Control and Its Applications

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In this paper, we obtain a bound on the error term of the solution to a control constrained, linear-quadratic optimal control problem over a clustered consensus network. For large scale systems, the solution may be regarded as computationally infeasible due to the increase in dimensionality. However, the two time-scale property of the network that arises from the cluster formation indicates that the optimal control problem can be written in standard singularly perturbed form. Thus, we are able to obtain a reduced dimension optimal control problem over a reduced dimension network where individual nodes within a cluster are collapsed into an aggregate node. The solution to the reduced problem can be shown to be asymptotically equivalent in the singular perturbation parameter δ to the solution of the original problem. However, for many values of δ this asymptotic result may fail to be of practical use. We improve on this result by applying a duality theory to the clustered network and derive an upper bound χu(δ) and lower bound χ l (δ) on the solution to the optimal control problem that holds for arbitrary δ and, furthermore, satisfies the inequality |χu(δ) − χ l (δ)| = O(δ) as δ → 0.

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Output containment control of heterogeneous multi-agent systems with leaders of bounded inputs: An adaptive finite-time observer approach

Yuan

Zeng

2019

Journal of the Franklin Institute

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Aggregate control of clustered networks with inter-cluster time delays

Cited by 12 publications

References 11 publications

Convergence Rates of Decentralized Gradient Methods over Cluster Networks

Convergence Rates of Decentralized Gradient Methods over Cluster Networks

Error bounds on the solution to an optimal control problem over clustered consensus networks

Output containment control of heterogeneous multi-agent systems with leaders of bounded inputs: An adaptive finite-time observer approach

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