Average consensus in matrix-weight-balanced digraphs




Allapanda, Chinnappa Yogesh B.

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This thesis investigates the average consensus of multi-agent systems with linear dynamics whose interconnections are modelled by balanced digraphs with matrix- weights. The thesis first introduces the notion of balanced digraphs and mirror graphs for matrix weights. Then it proves that the matrix-weight-balanced con- sensus controller is indeed globally asymptotically stable. The Lyapunov stability analysis exploits the properties of the mirror graph of a balanced digraph. Further, the necessary and sufficient condition for the system to achieve average consensus is shown to be positive definiteness of the matrix weights of its balanced digraph. Simulations with robots in SIMULINK verify that positive definite matrix weights on balanced graphs are indeed necessary and sufficient for average consensus. Fi- nally formation control of a multi-robot system is shown to be an application of the matrix-weight-balanced consensus algorithm using real time simulation of Clearpath Ridgeback robots in Gazebo and ROS.



Average Consensus, Matrix-Weight-Balanced, Lyapunov analysis, Mirror graph, Balanced digraph