Edge Agreement of Multi-agent System with Quantized Measurements via the Directed Edge Laplacian
This paper provides a theoretical foundation for edge agreement under quantization, which is important for control of multi-agent systems with limited communication, but the results are incremental as they extend existing edge agreement frameworks to quantized settings.
This work addresses the edge agreement problem for second-order nonlinear multi-agent systems with quantized measurements, introducing the essential edge Laplacian and a reduced model. For uniform quantizers, it provides an upper bound on the agreement neighborhood radius; for logarithmic quantizers, it proves exponential convergence to the desired equilibrium.
This work explores the edge agreement problem of second-order nonlinear multi-agent system under quantized measurements. Under the edge agreement framework, we introduce an important concept about the \emph{essential edge Laplacian} and also obtain a reduced model of the edge agreement dynamics based on the spanning tree subgraph. The quantized edge agreement problem of second-order nonlinear multi-agent system is studied, in which both uniform and logarithmic quantizers are considered. We do not only guarantee the stability of the proposed quantized control law, but also reveal the explicit mathematical connection of the quantized interval and the convergence properties for both uniform and logarithmic quantizers, which has not been addressed before. Particularly, for uniform quantizers, we provide the upper bound of the radius of the agreement neighborhood and indicate that the radius increases with the quantization interval. While for logarithmic quantizers, the agents converge exponentially to the desired agreement equilibrium. In addition, we figure out the relationship of the quantization interval and the convergence speed and also provide the estimates of the convergence rate. Finally, simulation results are given to verify the theoretical analysis.