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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2024-12-01
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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. |
| format | Article |
| id | doaj-art-cd9b51112e504d889f7596341f4a237f |
| institution | DOAJ |
| issn | 2076-0825 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Actuators |
| 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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