String stability under general topologies for CAVs: A coupled sliding surface-based distributed TMPC approach

Connected and Automated Vehicles (CAVs) are critical components of Intelligent Transportation Systems (ITS) to address traffic accidents and congestion and improve fuel economy. It remains an unsolved challenge to guarantee string stability for cooperative control of CAVs under general topologies. This study proposes a distributed tube-based model predictive control (TMPC) approach for string stable cooperative control of CAVs under general topologies by incorporating a novel string stable coupled sliding surface (CSS) as the terminal. This method is less restrictive and has a wider application range than existing string stable methods. First, a novel string stable CSS based on average spacing error and in-neighbor’s information is designed to guarantee string stability. Then, a TMPC controller is proposed to enforce the system dynamics to retain on the string stable CSS in a receding horizon manner. Specifically, the cost function, terminal constraints, and terminal assumed control input are appropriately designed to combine the string stable CSS with TMPC. Moreover, feasibility, closed-loop stability, and string stability are theoretically proved. Simulation results show that the proposed controller outperforms the state-of-the-art distributed model predictive control (DMPC) and TMPC methods in tracking performance and robustness.