TY - JOUR
T1 - Parabolic PDE-based multi-agent formation control on a cylindrical surface
AU - Qi, Jie
AU - Tang, Shu Xia
AU - Wang, Chuan
N1 - Funding Information:
National Natural Science Foundation of China [grant number 61134009, 61473265]; Natural Science Foundation of Shanghai [16ZR1401200]; Fundamental Research Funds for the Central Universities [2232015D3-24].
Publisher Copyright:
© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/1/2
Y1 - 2019/1/2
N2 - This paper considers the modelling and control design of the multi-agent systems in the 3-D space. The communication graph of the agents is a mesh-grid 2-D cylindrical surface. Different from most existing literatures, where the agents are modelled by ordinary differential equations (ODEs), we treat the agents as a continuum in this paper. More specifically, we model the collective dynamics of the agents by two reaction–advection–diffusion 2-D partial differential equations (PDEs). The PDE states represent the agent positions, and the equilibria correspond to possible formation manifolds. These PDEs can be open-loop unstable, and the boundary stabilisation problem of the PDEs on the cylindrical surface is solved using the backstepping method. An all-explicit observer-based output control scheme is constructed, which is distributed in the sense that each agent only needs local information. Closed-loop exponential stability in the L 2 , H 1 , and H 2 spaces is proved for the controller designs. Numerical simulations illustrate the effectiveness of our proposed approach.
AB - This paper considers the modelling and control design of the multi-agent systems in the 3-D space. The communication graph of the agents is a mesh-grid 2-D cylindrical surface. Different from most existing literatures, where the agents are modelled by ordinary differential equations (ODEs), we treat the agents as a continuum in this paper. More specifically, we model the collective dynamics of the agents by two reaction–advection–diffusion 2-D partial differential equations (PDEs). The PDE states represent the agent positions, and the equilibria correspond to possible formation manifolds. These PDEs can be open-loop unstable, and the boundary stabilisation problem of the PDEs on the cylindrical surface is solved using the backstepping method. An all-explicit observer-based output control scheme is constructed, which is distributed in the sense that each agent only needs local information. Closed-loop exponential stability in the L 2 , H 1 , and H 2 spaces is proved for the controller designs. Numerical simulations illustrate the effectiveness of our proposed approach.
KW - Backstepping
KW - boundary control
KW - cylindrical surface
KW - multi-agent formation control
KW - parabolic PDEs
UR - http://www.scopus.com/inward/record.url?scp=85017129214&partnerID=8YFLogxK
U2 - 10.1080/00207179.2017.1308556
DO - 10.1080/00207179.2017.1308556
M3 - Article
AN - SCOPUS:85017129214
VL - 92
SP - 77
EP - 99
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 1
ER -