A Directed Spanning Tree Adaptive Control Solution to Time-Varying Formations
D. Yue (Southeast University)
S Baldi (Southeast University, TU Delft - Team Bart De Schutter)
Jinde Cao (Southeast University)
Qi Li (Southeast University)
Bart De Schutter (TU Delft - Team Bart De Schutter, TU Delft - Delft Center for Systems and Control)
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Abstract
In this article, the time-varying formation and time-varying formation tracking problems are solved for linear multiagent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated with the digraph. The solution to these problems relies on an approach that generalizes the directed spanning tree (DST) 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.