Edge agreement of multi‐agent system with quantised measurements via the directed edge Laplacian
Zhiwen Zeng, Xiangke Wang, Zhiqiang Zheng · IET Control Theory and Applications · 2016
This work explores the edge agreement problem of second‐order non‐linear multi‐agent systems under quantised measurements. Under the edge agreement framework, the authors introduce an important concept about the essential edge Laplacian and also obtain a reduced model of the edge agreement dynamics based on the spanning tree subgraph. The quantised edge agreement problem of second‐order non‐linear multi‐agent systems is studied, in which both uniform and logarithmic quantisers are considered. The authors do not only guarantee the stability of the proposed quantised control law, but also reveal the explicit mathematical connection of the quantised interval and the convergence properties for both uniform and logarithmic quantisers, which has not been addressed before. Particularly, for uniform quantisers, they provide the upper bound of the radius of the agreement neighborhood and indicate that the radius increases with the quantisation interval. While for logarithmic quantisers, the agents converge exponentially to the desired agreement equilibrium. In addition, the authors figure out the relationship of the quantisation interval and the convergence speed and also provide the estimates of the convergence rate. Finally, simulation results are given to verify the theoretical analysis.