Distributed Platoon Control Under Topologies With Complex Eigenvalues: Stability Analysis and Controller Synthesis

The platooning of autonomous vehicles can significantly benefit road traffic. Most previous studies on platoon control have only focused on specific communication topologies, especially those with real eigenvalues. This paper extends existing studies on distributed platoon control to more generic topologies with complex eigenvalues, including both internal stability analysis and linear controller synthesis. Linear platoon dynamics are derived using an inverse vehicle model compensation, and graph theory is employed to model the communication topology, leading to an integrated high-dimension linear model of the closed-loop platoon dynamics. Using the similarity transformation, a sufficient and necessary condition is derived for the internal stability, which is completely defined in real number field. Then, we propose a Riccati inequality based algorithm to calculate the feasible static control gain. Further, disturbance propagation is formulated as an H-infinity performance, and the upper bound of spacing errors is explicitly derived using Lyapunov analysis. Numerical simulations with a nonlinear vehicle model validate the effectiveness of the proposed methods.