Leader selection for optimal network coherence

Patterson, Stacy; Bamieh, Bassam

doi:10.1109/cdc.2010.5718151

Cited by 130 publications

(185 citation statements)

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“…These algorithms, however, do not provide any guarantees on the optimality of the chosen set of leaders. Furthermore, while current approaches consider selecting a set of up to k leaders in static networks in order to minimize the error in the agent states, the problem of selecting the minimum-size set of leader agents to meet a given bound on the error, as well as leader selection in dynamic networks, is not studied in [47,82,108].…”

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

“…In [47] and [82], the authors propose a semidefinite programming relaxation of the problem of selecting a set of up to k leaders to minimize the H 2 -norm defined in [108]. These algorithms, however, do not provide any guarantees on the optimality of the chosen set of leaders.…”

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

“…Leader selection in the presence of noise in networks with static topology was considered in [108]. The authors of [108] introduce the network coherence metric, which measures how close the follower agents states are to their desired consensus values, and equals the H 2 -norm of the leader-follower system.…”

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

“…The authors of [108] introduce the network coherence metric, which measures how close the follower agents states are to their desired consensus values, and equals the H 2 -norm of the leader-follower system. It is shown that the network coherence is a monotone nonincreasing function of the leader set, and a greedy algorithm for maximizing the network coherence is presented.…”

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

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Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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Submodularity in Dynamics and Control of Networked Systems Andrew ClarkCo-Chairs of the Supervisory Committee:Radha Poovendran Electrical Engineering Linda Bushnell Electrical EngineeringControlling a networked dynamical system to reach a desired state is a fundamental challenge in applications including transportation, energy, social, and biological systems. One scalable approach to controlling such systems is to directly control the states of a subset of leader nodes, while relying on local interactions to steer the remaining nodes towards their desired states. The choice of leader nodes is known to affect system metrics including robustness to noise, rate of convergence to a desired state, and controllability of the system.Selecting an optimal subset of leader nodes, however, is inherently a combinatorial problem, making optimal leader node selection intractable in general.This thesis presents a submodular optimization framework to selecting leader nodes for control of networked systems. We investigate the problem of selecting a subset of leader nodes in order to minimize node state errors due to noise in the communication links between nodes. We prove that the error due to link noise is a supermodular function of the set of leader nodes, leading to the first polynomial-time algorithms for minimizing error due to link noise with provable optimality bounds. We develop our approach for networks with static topologies, as well as dynamic topologies due to random link failures, switching between predefined topologies, and arbitrary mobility.We study selecting leader nodes in order to minimize convergence error, defined as the error in the intermediate node states prior to reaching their desired values. We derive upper bounds for a class of convergence error metrics based on the hitting time of random walk on the network, which we prove to be a supermodular function of the set of input nodes.We present polynomial-time algorithms for minimizing convergence error with provable optimality bounds, for static as well as dynamic networks.Efficient algorithms have recently been proposed for selecting leader nodes to satisfy controllability, defined as the ability to drive the non-input nodes from any initial state to any desired state in finite time. These algorithms, however, do not incorporate performance criteria including robustness to noise and convergence rate. We study the problem of leader selection for joint performance and controllability, and prove that controllability can be formulated as a matroid constraint on the set of leader nodes. We propose efficient algorithms with provable optimality gap for selecting leader nodes for joint performance and controllability, and characterize the submodular structure of the largest controllable subgraph of a network.We also investigate selecting input nodes for guaranteeing synchronization in networked systems. Using the widely-studied Kuramoto model of nonlinear phase-coupled oscillators, we develop novel threshold-based conditions for a set of input nodes to ...

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Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

Section: Minimizing Errors Due To Link Noisementioning

confidence: 99%

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Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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“…The selection of effective leaders is therefore key and the problem has been considered by [2], [3] for achieving controllability and by [4], [5], [6] robustness by minimising the system error in the presence of noise. There are also contributions to the problem of achieving fast convergence through leadership.…”

Section: Introductionmentioning

confidence: 99%

Consensus speed optimisation with finite leadership perturbation in k-nearest neighbour networks

Clark

Punzo

Macdonald

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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This version is available at https://strathprints.strath.ac.uk/65072/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Consensus Speed Optimisation with Finite Leadership Perturbation in k-Nearest Neighbour Networks Ruaridh Clark, Giuliano Punzo and Malcolm MacdonaldAbstract-Near-optimal convergence speeds are found for perturbed networked systems, with N interacting agents that conform to k-nearest neighbour (k-NNR) connection rules, by allocating a finite leadership resource amongst selected nodes. These nodes continue averaging their state with that of their neighbours while being provided with the resources to drive the network to a new state. Such systems are represented by a directed graph Laplacian with two newly presented semianalytical approaches used to maximise the consensus speed. The two methods developed typically produce near-optimal results and are highly efficient when compared with conventional numerical optimisation, where the asymptotic computational complexity is O(n 3 ) and O(n 4 ) respectively. The upper limit for the convergence speed of a perturbed k-NNR network is identified as the largest element of the first left eigenvector (FLE) of a graph's adjacency matrix. The first semi-analytical method exploits this knowledge by distributing leadership resources amongst the most prominent nodes highlighted by this FLE. The second method relies on the FLEs of manipulated versions of the adjacency matrix to expose different communities of influential nodes. These are shown to correspond with the communities found by the Leicht-Newman detection algorithm, with this method enabling optimal leadership selection even in low outdegree (< 12 connections) graphs, where the first semianalytical method is less effective.

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Koopman Performance Analysis of Nonlinear Consensus Networks

Mousavi

Somarakis

Sun³

et al. 2020

Lecture Notes in Control and Information Sciences

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Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative protocols, which consist of multiple agents that are coupled together via an undirected state-dependent graph. We develop a representation of the system solution by decomposing the nonlinear system utilizing ideas from the Koopman operator theory and its spectral analysis. We use recent results on the extensions of the wellknown Hartman theorem for hyperbolic systems to establish a connection between the original nonlinear dynamics and the linearized dynamics in terms of Koopman spectral properties. The expected value of the output energy of the nonlinear protocol, which is related to the notions of coherence and robustness in dynamical networks, is evaluated and characterized in terms of Koopman eigenvalues, eigenfunctions, and modes. Spectral representation of the performance measure enables us to develop algorithmic methods to assess the performance of this class of nonlinear dynamical networks as a function of their graph topology. Finally, we propose a scalable computational method for approximation of the components of the Koopman mode decomposition, which is necessary to evaluate the systemic performance measure of the nonlinear dynamic network.

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Leader selection for optimal network coherence

Cited by 130 publications

References 12 publications

Submodularity in Dynamics and Control of Networked Systems

Submodularity in Dynamics and Control of Networked Systems

Consensus speed optimisation with finite leadership perturbation in k-nearest neighbour networks

Koopman Performance Analysis of Nonlinear Consensus Networks

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