Evyatar Matmon is finishing up his MSc thesis work within the Technion Autonomous Systems Program (TASP) (TASP). As part of his degree requirements he gave a wonderful seminar on his results.
Abstract The consensus protocol is fundamental multi-agent systems protocol which enables synchronization of state trajectories. In semi-autonomous consensus protocols, selected agents, called leaders, receive external inputs, while others, the followers, rely only on interactions with their neighbors. This work addresses the problem of leader identification—determining the leader nodes by observing only agent trajectories. Using the system dynamics, we focus on analyzing the Fiedler vector, associated with the smallest non-zero eigenvalue of the interconnection matrix. Our approach involves analyzing a sequence of graphs with increasing number of nodes and the associated Fiedler vectors. We demonstrate that the components of the Fiedler vector converge to a quantity related to the degree of each node. We then provide a sufficient condition for sufficiently large graphs to achieve a separation of the Fiedler vector components into two distinct groups corresponding to the leaders and followers. We use this result to provide an estimation algorithm of the leader nodes by using only measurements of agent velocities. We also provide some numerical studies to demonstrate our results.
