Controllability of homogeneous single-leader networks

This paper addresses an aspect of controllability in a single-leader network when the agents are homogeneous. In such a network, indices are not assigned to the individual agents and controllability, which is typically a point to point property, now becomes a point to set property, where the set consists of all permutations of the target point. Agent homogeneity allows for choice of the optimal target point permutation that minimizes the distance to the system's reachable subspace, which we show is equivalent to finding a minimum sum-of-squares clustering with constraints on the cluster sizes. However, finding the optimal permutation is NP-hard. Methods are presented to find suboptimal permutations in the general case and the optimal permutation when the agent positions are 1-D.