A Directed Spanning Tree Adaptive Control Solution to Time-Varying Formations
Dongdong Yue, Simone Baldi, Jinde Cao, Qi Li, Bart De Schutter
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.
Topics & Concepts
DigraphSpanning treeLaplacian matrixDirected graphStrongly connected componentEigenvalues and eigenvectorsConvergence (economics)Multi-agent systemGraph theoryMathematicsLinear systemGraphMathematical optimizationComputer scienceDiscrete mathematicsCombinatoricsArtificial intelligenceEconomic growthPhysicsMathematical analysisEconomicsQuantum mechanicsDistributed Control Multi-Agent SystemsNeural Networks Stability and SynchronizationMathematical and Theoretical Epidemiology and Ecology Models