Optimal Periodic Control of Connected Multiple Vehicles with Heterogeneous Dynamics and Guaranteed Bounded Stability

The platooning of connected and automated vehicles has the potential to significantly improve the fuel efficiency of road transportation. Shortening the carfollowing distance to reduce aerodynamic drag is often used to improve fuel economy in today's platoons, but suffers high risk of rear-end collision. This paper presents an alternative solution to reduce platoon fuel consumption, i.e., periodic longitudinal control, which remains effective under the condition of middle or long following distance. The periodic controller can be applied to heterogeneous platoons, in which the optimal switching rule is designed for each vehicle to maintain a safe following distance while guaranteeing a collective bounded stability. Sectionalized switching maps based on state trajectory analysis are designed to choose the appropriate driving mode. The bounded stability for heterogeneous platoons is proved through the set-invariance theory, which ensures that the inter-vehicle distances are confined in a desirable range. Simulation results show that the proposed method can save up to 18% fuel compared to linear quadratic (LQ) controller, and all vehicles achieve bounded range error and velocity fluctuation.