Delay Range for Consensus Achievable by Proportional and PD Feedback Protocols With Time-Varying Delays

This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure...

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Published inIEEE transactions on automatic control Vol. 67; no. 6; pp. 3212 - 3219
Main Author Ma, Dan
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Delay
Delays
Eigenvalues and eigenfunctions
Graph theory
Lower bounds
Maximal delay range
Multiagent systems
PD control
Power system dynamics
Proportional derivative
proportional-derivative (PD) protocol
Protocols
robust consensus
Robustness
Time varying control
time-varying delay
Topology
Online AccessGet full text
ISSN0018-9286
1558-2523
DOI10.1109/TAC.2021.3096899

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Abstract This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula>-type small-gain analysis to multiagent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by the P protocol by incorporating the delay variation rate in the design of the PD control protocol.
AbstractList This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an [Formula Omitted]-type small-gain analysis to multiagent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by the P protocol by incorporating the delay variation rate in the design of the PD control protocol.
This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control protocols subject to time-varying delays. The maximal delay range is defined by the delay consensus margin (DCM), which is a robustness measure within which consensus can be achieved robustly despite the presence of uncertain and time-varying delays. We apply an <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula>-type small-gain analysis to multiagent systems, which results in explicit lower bounds on the DCM for both undirected and directed graphs. The results provide sufficient conditions for robust consensus for all time-varying delays that may vary within the range. It is seen that the agent dynamics and the graph connectivity may fundamentally limit the range of tolerable delays. It is also found that the DCM can be increased beyond that achieved by the P protocol by incorporating the delay variation rate in the design of the PD control protocol.
Author Ma, Dan
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Snippet This article examines the delay range for robust consensus of unstable first-order agents by using proportional (P) and proportional-derivative (PD) control...
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SubjectTerms Delay
Delays
Eigenvalues and eigenfunctions
Graph theory
Lower bounds
Maximal delay range
Multiagent systems
PD control
Power system dynamics
Proportional derivative
proportional-derivative (PD) protocol
Protocols
robust consensus
Robustness
Time varying control
time-varying delay
Topology
Title Delay Range for Consensus Achievable by Proportional and PD Feedback Protocols With Time-Varying Delays
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Volume 67
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