Parabolic PDE-based multi-agent formation control on a cylindrical surface

Jie Qi, Shu Xia Tang, Chuan Wang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)77-99
Number of pages23
JournalInternational Journal of Control
Issue number1
StatePublished - Jan 2 2019


  • Backstepping
  • boundary control
  • cylindrical surface
  • multi-agent formation control
  • parabolic PDEs


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