Stability and robustness of large platoons of vehicles with double‐integrator models and nearest neighbor interaction

SUMMARY We study the stability and robustness of a large platoon of vehicles, where each vehicle is modeled as a double integrator, for two decentralized control architectures: predecessor following and symmetric bidirectional. In the predecessor‐following architecture, the control action on each agent only depends on the information from its immediate front neighbor, whereas in the symmetric bidirectional architecture, it depends equally on the information from both its immediate front neighbor and back neighbor. We prove asymptotic stability of the formation for a class of nonlinear controllers with sector nonlinearity, with the linear controller as a special case. We show that the convergence rate of the predecessor‐following architecture is much faster than that of the symmetric bidirectional architecture. However, the predecessor‐following architecture suffers high algebraic growth of initial errors. We also establish scaling laws (with N ) of certain H ∞ norms of the formation that measure its robustness to external disturbances for the linear case. It is shown that the robustness performance grows geometrically in N for predecessor‐following architecture but only polynomially in N for symmetric‐bidirectional architecture. Extensive numerical simulations are conducted to verify the predictions for the linear case and empirically estimate the corresponding performance metrics for a saturation‐type nonlinear controller. On the basis of the analytical and numerical results, it is seen that the symmetric bidirectional architecture outperforms the predecessor‐following architecture in all measures of performance. Within the predecessor‐following architecture, the nonlinear controller is seen to perform better in general than the linear one. A number of design guidelines are provided on the basis of these conclusions. Copyright © 2012 John Wiley & Sons, Ltd.