Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems

In this study, the cyclic pursuit formation stabilization problem in target-enclosing operations by multiple homogeneous dynamic agents is investigated. To this end, a Lyapunov <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><seman...

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Main Authors: Jun-Gyu Park, Yeongjae Kim, Tae-Hyoung Kim
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Actuators
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Online Access:https://www.mdpi.com/2076-0825/13/12/495
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author Jun-Gyu Park
Yeongjae Kim
Tae-Hyoung Kim
author_facet Jun-Gyu Park
Yeongjae Kim
Tae-Hyoung Kim
author_sort Jun-Gyu Park
collection DOAJ
description In this study, the cyclic pursuit formation stabilization problem in target-enclosing operations by multiple homogeneous dynamic agents is investigated. To this end, a Lyapunov <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>-stability problem is first formulated to cover the transient performance requirements for multi-agent systems. Then, a simple diagrammatic Lyapunov <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>-stability criterion for cyclic pursuit formation is derived. The formation control scheme combined with a cyclic-pursuit-based distributed online path generator satisfying this condition guarantees both the required transient performance and global convergence properties with theoretical rigor. It is shown that the maximization of the connectivity gain in a cyclic-pursuit-based online path generator can be reduced to an optimization problem subject to linear matrix inequality constraints derived using the generalized Kalman-Yakubovich–Popov lemma. This approach provides a permissible range of connectivity gain, which not only guarantees global formation stability/convergence properties but also satisfies the required performance specification. Several numerical examples are provided to confirm the effectiveness of the proposed method.
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spelling doaj-art-cd9b51112e504d889f7596341f4a237f2025-08-20T02:55:31ZengMDPI AGActuators2076-08252024-12-01131249510.3390/act13120495Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent SystemsJun-Gyu Park0Yeongjae Kim1Tae-Hyoung Kim2Department of Mechanical Engineering, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul 06974, Republic of KoreaDepartment of Mechanical Engineering, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul 06974, Republic of KoreaDepartment of Mechanical Engineering, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul 06974, Republic of KoreaIn this study, the cyclic pursuit formation stabilization problem in target-enclosing operations by multiple homogeneous dynamic agents is investigated. To this end, a Lyapunov <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>-stability problem is first formulated to cover the transient performance requirements for multi-agent systems. Then, a simple diagrammatic Lyapunov <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula>-stability criterion for cyclic pursuit formation is derived. The formation control scheme combined with a cyclic-pursuit-based distributed online path generator satisfying this condition guarantees both the required transient performance and global convergence properties with theoretical rigor. It is shown that the maximization of the connectivity gain in a cyclic-pursuit-based online path generator can be reduced to an optimization problem subject to linear matrix inequality constraints derived using the generalized Kalman-Yakubovich–Popov lemma. This approach provides a permissible range of connectivity gain, which not only guarantees global formation stability/convergence properties but also satisfies the required performance specification. Several numerical examples are provided to confirm the effectiveness of the proposed method.https://www.mdpi.com/2076-0825/13/12/495multi-agent dynamical systemsformation controlgeneralized Kalman–Yakubovich–Popov lemmalinear matrix inequality
spellingShingle Jun-Gyu Park
Yeongjae Kim
Tae-Hyoung Kim
Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
Actuators
multi-agent dynamical systems
formation control
generalized Kalman–Yakubovich–Popov lemma
linear matrix inequality
title Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
title_full Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
title_fullStr Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
title_full_unstemmed Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
title_short Distributed Coordination <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">D</mi></semantics></math></inline-formula>-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems
title_sort distributed coordination inline formula math display inline semantics mi mathvariant bold script d mi semantics math inline formula stabilization in cyclic pursuit formations of dynamical multi agent systems
topic multi-agent dynamical systems
formation control
generalized Kalman–Yakubovich–Popov lemma
linear matrix inequality
url https://www.mdpi.com/2076-0825/13/12/495
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