Analysis of containment control for multi-agent systems based on broadcast gossip algorithm
Zhuangzhuang Ma, Hongjian Chen, Lei Shi, Jinliang Shao · 2019
This paper investigates the containment control problem for multi-agent systems based on the broadcast gossip algorithm, in which only one agent wakes up in the light of the asynchronous time model at each time and sends its information, and one part of the remaining agents get the message to update their states while the other part keep the states unchanged. We equivalently transform the algorithm into a mathematical model with the matrix-vector form, then conduct a detailed theoretical analysis for the mathematical model by utilizing tools including graph theory and stochastic matrix. Then, we establish a necessary and sufficient algebraic graph condition to ensure that every follower gradually enters the convex hull spanned by the leaders. Finally, we give a numerical example to argument the validity of theoretical result.