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

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

doi:10.1109/TCNS.2021.3050332

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

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

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

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 language	English
Journal	IEEE Transactions on Control of Network Systems
DOIs	https://doi.org/10.1109/TCNS.2021.3050332
Publication status	Accepted/In press - 8 Jan 2021

Keywords

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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10.1109/TCNS.2021.3050332

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title = "A Directed Spanning Tree Adaptive Control Solution to Time-Varying Formations",

abstract = "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.",

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AU - Baldi, Simone

AU - Cao, Jinde

AU - Li, Qi

AU - De Schutter, Bart

PY - 2021/1/8

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N2 - 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.

AB - 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.

KW - Adaptive control

KW - Control systems

KW - directed graphs

KW - Eigenvalues and eigenfunctions

KW - formation control

KW - Laplace equations

KW - Multi-agent systems

KW - multi-agent systems

KW - Symmetric matrices

KW - Time-varying systems

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