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On the Role of Homogeneity When Controlling Single‐Leader Networks

This paper presents an approach to controlling agent positions in single‐leader networks to target points while explicitly taking agent homogeneity into account. When the capabilities of agents to accomplish tasks at each of the targets are identical, then the label of the target points may be permuted while still expressing the same intention. In single‐leader networks which are not completely controllable, such a permutation of the target points may at times move a target closer to the system's reachable subspace, thereby allowing the network to surpass the limitations on controllability when homogeneity is not considered explicitly. To fully exploit this property in homogeneous networks, it is then necessary to find the permutation of a target point which brings it closest to the reachable subspace. However, finding this optimal permutation is shown to be in general a non‐deterministic polynomial‐time (NP)‐hard problem. Specific network topologies are identified for when finding such an optimal permutation of a target point can be advantageous when controlling single‐leader networks. Moreover, an alternate view of the problem of finding optimal permutations is presented in which clustering‐based algorithms can be applied to find suboptimal solutions.