Nonlinear Network Modes in Cyclic Systems with Applications to Connected Vehicles

In this paper, we propose a novel technique to decompose networked systems with cyclic structure into nonlinear modes and apply these ideas to a system of connected vehicles. We perform linear and nonlinear transformations that exploit the network structure and lead to nonlinear modal equations that are decoupled. Each mode can be obtained by solving a small set of algebraic equations without deriving the coefficients for any other mode. By focusing on the mode that is loosing stability, bifurcation analysis can be carried out. The techniques developed are applied to evaluate the impact of connected cruise control on the nonlinear dynamics of a connected vehicle system.