Consensus Robustness Margins of First-Order Agents over Undirected Graphs

Yanling Ding; Dan Ma; Qi Mao; Hui Peng; Jie Chen

doi:10.1109/TAC.2023.3321795

Consensus Robustness Margins of First-Order Agents over Undirected Graphs

Yanling Ding
, Dan Ma
, Qi Mao^*
, Hui Peng
, Jie Chen

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

This article concerns robust consensus problems for continuous-time first-order multi-agent systems with respect to uncertain gain and phase of the agent's frequency response varying within certain ranges. We consider dynamic output feedback control protocol in the form of proportional–integral (PI) control. The agents can in general be nonminimum phase and unstable systems, which are interconnected by an undirected graph network. We seek to determine the largest ranges of gain and phase variations, referred to as the gain consensus margin (GCM) and the phase consensus margin (PCM), respectively, so that consensus can be achieved robustly by PI protocols within these ranges. Our main results consist of explicit analytical expressions of the GCM and PCM achievable by PI protocols, which demonstrate how the agent's unstable pole and nonminimum phase zero, as well as the network connectivity may confine the gain and phase variation ranges so that consensus can or cannot be maintained. © 2023 IEEE.

Original language	English
Pages (from-to)	3262-3269
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	69
Issue number	5
Online published	3 Oct 2023
DOIs	https://doi.org/10.1109/TAC.2023.3321795
Publication status	Published - May 2024

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 62121004, 61906047, and 61973060, in part by the Hong Kong RGC under the project under Grants CityU 11203321 and CityU 11213322, and in part by the City University of Hong Kong under Grant 9380054. An earlier version of this paper was presented in part at the 2023 American Control Conference (ACC) [DOI: 10.23919/ACC55779.2023.10155788].

Research Keywords

gain consensus margin
multi-agent systems
Output feedback
output PI control protocol
Phase change materials
phase consensus margin
Poles and zeros
Protocols
Robustness
Robustness analysis
stability margin
Uncertainty
Gain consensus margin (GCM)
multi-agent systems (MASs)
phase consensus margin (PCM)
output proportional–integral (PI) control protocol

RGC Funding Information

RGC-funded

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title = "Consensus Robustness Margins of First-Order Agents over Undirected Graphs",

abstract = "This article concerns robust consensus problems for continuous-time first-order multi-agent systems with respect to uncertain gain and phase of the agent's frequency response varying within certain ranges. We consider dynamic output feedback control protocol in the form of proportional–integral (PI) control. The agents can in general be nonminimum phase and unstable systems, which are interconnected by an undirected graph network. We seek to determine the largest ranges of gain and phase variations, referred to as the gain consensus margin (GCM) and the phase consensus margin (PCM), respectively, so that consensus can be achieved robustly by PI protocols within these ranges. Our main results consist of explicit analytical expressions of the GCM and PCM achievable by PI protocols, which demonstrate how the agent's unstable pole and nonminimum phase zero, as well as the network connectivity may confine the gain and phase variation ranges so that consensus can or cannot be maintained. {\textcopyright} 2023 IEEE.",

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author = "Yanling Ding and Dan Ma and Qi Mao and Hui Peng and Jie Chen",

year = "2024",

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doi = "10.1109/TAC.2023.3321795",

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T1 - Consensus Robustness Margins of First-Order Agents over Undirected Graphs

AU - Ding, Yanling

AU - Ma, Dan

AU - Mao, Qi

AU - Peng, Hui

AU - Chen, Jie

PY - 2024/5

Y1 - 2024/5

N2 - This article concerns robust consensus problems for continuous-time first-order multi-agent systems with respect to uncertain gain and phase of the agent's frequency response varying within certain ranges. We consider dynamic output feedback control protocol in the form of proportional–integral (PI) control. The agents can in general be nonminimum phase and unstable systems, which are interconnected by an undirected graph network. We seek to determine the largest ranges of gain and phase variations, referred to as the gain consensus margin (GCM) and the phase consensus margin (PCM), respectively, so that consensus can be achieved robustly by PI protocols within these ranges. Our main results consist of explicit analytical expressions of the GCM and PCM achievable by PI protocols, which demonstrate how the agent's unstable pole and nonminimum phase zero, as well as the network connectivity may confine the gain and phase variation ranges so that consensus can or cannot be maintained. © 2023 IEEE.

AB - This article concerns robust consensus problems for continuous-time first-order multi-agent systems with respect to uncertain gain and phase of the agent's frequency response varying within certain ranges. We consider dynamic output feedback control protocol in the form of proportional–integral (PI) control. The agents can in general be nonminimum phase and unstable systems, which are interconnected by an undirected graph network. We seek to determine the largest ranges of gain and phase variations, referred to as the gain consensus margin (GCM) and the phase consensus margin (PCM), respectively, so that consensus can be achieved robustly by PI protocols within these ranges. Our main results consist of explicit analytical expressions of the GCM and PCM achievable by PI protocols, which demonstrate how the agent's unstable pole and nonminimum phase zero, as well as the network connectivity may confine the gain and phase variation ranges so that consensus can or cannot be maintained. © 2023 IEEE.

KW - gain consensus margin

KW - multi-agent systems

KW - Output feedback

KW - output PI control protocol

KW - Phase change materials

KW - phase consensus margin

KW - Poles and zeros

KW - Protocols

KW - Robustness

KW - Robustness analysis

KW - stability margin

KW - Uncertainty

KW - Gain consensus margin (GCM)

KW - multi-agent systems (MASs)

KW - phase consensus margin (PCM)

KW - output proportional–integral (PI) control protocol

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M3 - RGC 21 - Publication in refereed journal

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EP - 3269

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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ER -

Consensus Robustness Margins of First-Order Agents over Undirected Graphs

Abstract

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Research Keywords

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GRF: Performance and Robustness of Multi-Agent Control Systems

GRF: Localization and Detection toward Securing Networked Control Systems

Cite this

Consensus Robustness Margins of First-Order Agents over Undirected Graphs

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

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Projects

GRF: Performance and Robustness of Multi-Agent Control Systems

GRF: Localization and Detection toward Securing Networked Control Systems

Cite this