Formation deployment control of multi-agent systems modeled with PDE
In this paper, the formation control problem of PDE-based multi-agent systems (MASs) is discussed. Firstly, the MASs are developed on a one-dimensional chain topology based on the polar coordinate system, and the dynamics of MASs is simulated using the spatial-varying coefficient wave equation. Seco...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022632?viewType=HTML |
| _version_ | 1828110240789299200 |
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| author | Sai Zhang Li Tang Yan-Jun Liu |
| author_facet | Sai Zhang Li Tang Yan-Jun Liu |
| author_sort | Sai Zhang |
| collection | DOAJ |
| description | In this paper, the formation control problem of PDE-based multi-agent systems (MASs) is discussed. Firstly, the MASs are developed on a one-dimensional chain topology based on the polar coordinate system, and the dynamics of MASs is simulated using the spatial-varying coefficient wave equation. Secondly, a boundary control scheme is proposed by combining PDE-backstepping technique and the Volterra integral transformation. The well-posedness of kernel function is proved by using the iterative and inductive methods. Then, the stability of the closed-loop system is proved by using Lyapunov direct method. Finally, the PDE model is discretized using the finite difference method, and the distributed cooperative control protocol is obtained, in which the followers only need to know the location information of themselves and their neighbors. With this control protocol, leaders drive the MAS to stabilize in the desired formation. Both theoretical analysis and numerical simulation prove that the proposed control scheme is effective. |
| first_indexed | 2024-04-11T11:16:41Z |
| format | Article |
| id | doaj.art-ec5e74a8a68849dc8feba2f230765168 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-11T11:16:41Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-ec5e74a8a68849dc8feba2f2307651682022-12-22T04:27:13ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-09-011912135411355910.3934/mbe.2022632Formation deployment control of multi-agent systems modeled with PDESai Zhang0Li Tang1Yan-Jun Liu2College of Science, Liaoning University of Technology, Jinzhou 121001, ChinaCollege of Science, Liaoning University of Technology, Jinzhou 121001, ChinaCollege of Science, Liaoning University of Technology, Jinzhou 121001, ChinaIn this paper, the formation control problem of PDE-based multi-agent systems (MASs) is discussed. Firstly, the MASs are developed on a one-dimensional chain topology based on the polar coordinate system, and the dynamics of MASs is simulated using the spatial-varying coefficient wave equation. Secondly, a boundary control scheme is proposed by combining PDE-backstepping technique and the Volterra integral transformation. The well-posedness of kernel function is proved by using the iterative and inductive methods. Then, the stability of the closed-loop system is proved by using Lyapunov direct method. Finally, the PDE model is discretized using the finite difference method, and the distributed cooperative control protocol is obtained, in which the followers only need to know the location information of themselves and their neighbors. With this control protocol, leaders drive the MAS to stabilize in the desired formation. Both theoretical analysis and numerical simulation prove that the proposed control scheme is effective.https://www.aimspress.com/article/doi/10.3934/mbe.2022632?viewType=HTMLformation controlmulti-agent systemswave pdepde-backsteppingleader-follower |
| spellingShingle | Sai Zhang Li Tang Yan-Jun Liu Formation deployment control of multi-agent systems modeled with PDE Mathematical Biosciences and Engineering formation control multi-agent systems wave pde pde-backstepping leader-follower |
| title | Formation deployment control of multi-agent systems modeled with PDE |
| title_full | Formation deployment control of multi-agent systems modeled with PDE |
| title_fullStr | Formation deployment control of multi-agent systems modeled with PDE |
| title_full_unstemmed | Formation deployment control of multi-agent systems modeled with PDE |
| title_short | Formation deployment control of multi-agent systems modeled with PDE |
| title_sort | formation deployment control of multi agent systems modeled with pde |
| topic | formation control multi-agent systems wave pde pde-backstepping leader-follower |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022632?viewType=HTML |
| work_keys_str_mv | AT saizhang formationdeploymentcontrolofmultiagentsystemsmodeledwithpde AT litang formationdeploymentcontrolofmultiagentsystemsmodeledwithpde AT yanjunliu formationdeploymentcontrolofmultiagentsystemsmodeledwithpde |