A Directed Spanning Tree Adaptive Control Solution to Time-Varying Formations

Dongdong Yue, Simone Baldi, Jinde Cao, Qi Li, Bart De Schutter

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In this paper, the time-varying formation and time-varying formation tracking problems are solved for linear multi-agent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated to the digraph. The solution to these problems relies on an approach that generalizes the directed spanning tree adaptive method, which was originally limited to consensus problems. Necessary and sufficient conditions for the existence of solutions to the formation problems are derived. Asymptotic convergence of the formation errors is proved via graph theory and Lyapunov analysis.

Original languageEnglish
Pages (from-to)690-701
JournalIEEE Transactions on Control of Network Systems
Issue number2
Publication statusPublished - 2021

Bibliographical note

Accepted Author Manuscript


  • Adaptive control
  • Control systems
  • directed graphs
  • Eigenvalues and eigenfunctions
  • formation control
  • Laplace equations
  • Multi-agent systems
  • multi-agent systems
  • Symmetric matrices
  • Time-varying systems


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