On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

Moradian, Hossein; Kia, Solmaz S.

doi:10.1109/tcns.2018.2863568

Cited by 41 publications

(16 citation statements)

References 41 publications

(92 reference statements)

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“…The Lambert W function has been used to in stability analysis, eigenvalue assignment and obtaining the rate of convergence of linear time-delayed systems [4], [20]- [22]. For a z ∈ C, the Lambert W function is defined as the solution of s e s = z, i.e., s = W (z).…”

Section: A Review Of Properties Of Lambert W Functionmentioning

confidence: 99%

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

Moradian

Kia

2020

IEEE Trans. Automat. Contr.

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This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked systems by use of a delayed feedback.

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Section: A Review Of Properties Of Lambert W Functionmentioning

confidence: 99%

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

Moradian

Kia

2020

IEEE Trans. Automat. Contr.

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“…This problem is called the dynamic average consensus. The objective is this class of problems is not to converge to an exact average of initial states, but to converge to the neighbourhood of the time varying average of the state of robots in the network [38,16,9,2,8,32].…”

Section: Static Vs Dynamic Reference Average Consensusmentioning

confidence: 99%

“…For the average scalar-weighted-consensus case both communication and input delay have been considered in existing literature. [32], [61].…”

Section: Delayed Networkmentioning

confidence: 99%

Average Consensus in Matrix-Weight-Balanced Digraphs

Chinnappa

Constantinescu

2019

2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)

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This thesis investigates the average consensus of multi-agent systems with linear dynamics whose interconnections are modelled by balanced digraphs with matrixweights. The thesis first introduces the notion of balanced digraphs and mirror graphs for matrix weights. Then it proves that the matrix-weight-balanced consensus controller is indeed globally asymptotically stable. The Lyapunov stability analysis exploits the properties of the mirror graph of a balanced digraph. Further, the necessary and sufficient condition for the system to achieve average consensus is shown to be positive definiteness of the matrix weights of its balanced digraph. Simulations with robots in SIMULINK verify that positive definite matrix weights on balanced graphs are indeed necessary and sufficient for average consensus. Finally formation control of a multi-robot system is shown to be an application of the matrix-weight-balanced consensus algorithm using real time simulation of Clearpath Ridgeback robots in Gazebo and ROS.

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“…In spite of significant progress on DAT, the study on practical issues, such as delay and noise, is only to emerge [30]. Indeed, it is generally recognized, and intuitively clear, that the convergence of DAT algorithms can be constrained by transmission failures, input delays, as well as reference noise, which all likely result in negative effect on the convergence of the closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

Delay and Packet-Drop Tolerant Multi-Stage Distributed Average Tracking in Mean Square

Chen¹,

Changjiang²,

Guo³

et al. 2020

Preprint

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This paper studies the distributed average tracking problem pertaining to a discrete-time linear timeinvariant multi-agent network, which is subject to, concurrently, input delays, random packet-drops, and reference noise. The problem amounts to an integrated design of delay and packet-drop tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multi-stage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling distributed average tracking algorithm that is robust to initialization error and allows the trade-off between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

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On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

Cited by 41 publications

References 41 publications

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

Average Consensus in Matrix-Weight-Balanced Digraphs

Delay and Packet-Drop Tolerant Multi-Stage Distributed Average Tracking in Mean Square

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