Quantized Leaderless and Leader-Following Consensus of High-Order Multi-Agent Systems With Limited Data Rate

Distributed consensus with limited communication data rate is an interesting and important problem and has been studied for multi-agent networks with the first order and second order integrator dynamics. However, the problem remains challenging for higher-order systems due to the complexity of consensus analysis and data rate minimization. In this paper, the leaderless and leader-following quantized consensus for a special kind of high-order systems are considered. Each agent is assumed to be controllable and observable with single input and single output, and its system matrix admits n identical eigenvalues of 1. The special case of n-th order integrator multi-agent system with only the first state variable being measurable is first investigated, and it is shown that for a fixed undirected connected network, n bits of information exchange between agents suffice to guarantee the leaderless and leader-following quantized consensus respectively with an exponential convergence rate by employing a suitable encoding-decoding scheme and perturbation analysis of matrices. The obtained results are then extended to the general case of multi-agent dynamics with n identical eigenvalues of 1 by applying the same encoding-decoding scheme and control protocol to an observer system for each agent. The final consensus value and the application to formation control are also discussed.