Document Type



Master of Science


Electrical Engineering

First Adviser

Motee, Nader


In this thesis, we analyze multi-agent systems under the leader/follower control scheme. We take a graph-theoretic approach to defining the system which allows us to create a state-space representation of the agents. Using this model we can consider the group of agents as a linear time-invariant system under point mass dynamics. Linear control theory is used to examine the controllability of these systems. Uncontrollability from graph topology and symmetry is also explored. The process of electing both an optimal leader and set of optimal leaders to bring the agents to a consensus is investigated. Conditions of optimality require the leaders to minimize a cost function while simultaneously leading to a controllable network. At the end, we decompose the cost index in such a way as to show its relation to the underlying commutation graph of the network and the desired location of the agents. Finally, we demonstrate how varying the weights and the leader configuration affects the performance of the network.