Reduced-order approximation of consensus dynamics in networks with a hybrid adaptive communication protocol

This paper focuses on a hybrid adaptive control (or communication protocol) that is used to drive a network of agents towards consensus. We develop an approximation to the system to capture the qualitative behaviour of the most distant node state and gain dynamics, thus serving as a powerful reduction of order of the larger system. Numerical results are presented to argue the robustness of the approximation over a range of differing initial network sizes and distributions of initial state values.