Consensus speed maximisation in engineered swarms with autocratic leaders

Control of a large engineered swarm can be achieved by influencing key agents within the swarm. The swarm can rely on its communication network to spread the external perturbation and transition to a new state when all agents reach a consensus. Maximising this consensus speed is a vital design parameter when fast response is desirable. The systems analysed consist of N interacting agents that have the same number of outward, observing, connections that follow k-nearest neighbour rules and are represented by a directed graph Laplacian. The spectral properties of this graph are exploited to identify leaders with a newly presented semi-analytical approach referred to as the Leaders of Influence (LoI) method. This method is demonstrated on k-NNR graphs for a set number of leaders. These methods are compared with a genetic algorithm and are shown to be efficient and effective at leader identification. A focus of this work is the effect of leadership style on consensus speed where an autocratic approach (leaders that are not influenced by other nodes in the graph) is shown to always produce faster consensus than a democratic leadership model.