Optimal design of cyclic pursuit weights in hierarchical multi-agent systems

We consider an average consensus problem for multi-agent systems based on a two-layer hierarchical cyclic pursuit update scheme in discrete time. The aim is to achieve a faster rate of convergence and in particular to minimize the size of the dominating eigenvalue of the system. This is done by finding (i) the appropriate grouping for the given number of agents and then (ii) the optimal weights to be employed in the update scheme of each agent. We provide a general solution for this problem, which indicates that conventional weights are optimal only in certain cases. Numerical examples are given to illustrate the effectiveness of the results.