Performance analysis for multi-agent coordination with partial measurable states over digital networks

In this paper, we consider the performance of a class of distributed coordination algorithms of discrete-time second-order multi-agent systems with partially measurable states and a limited communication data rate. The distributed coordinated control law is based on an encoding-decoding scheme which integrates the state observation with encoding/decoding. The convergence time, the selection of controller parameters and the performance limit are discussed. We give upper bounds of the convergence time in terms of precision, control and network parameters. We develop a linear approximation of the spectral radius of the closed-loop matrix with respect to the control gains and the algebraic connectivity of the communication graph, by which we show that for a connected network, 2-bit quantizers suffice for the exponential asymptotic synchronization of the states of the agents. Furthermore, it is shown that as the number of agents increases, the asymptotic convergence rate can be approximated as a function of the number of agents, the number of quantization levels (communication data rate) and the ratio of the algebraic connectivity to the spectral radius of the Laplacian matrix of the communication graph.