Robust Longitudinal Distributed Model Predictive Control of Connected and Automated Vehicles with Coupled Safety Constraints

This paper deals with robust cooperative control of connected and automated vehicles (CAVs) with special consideration of the coupled safety inter-vehicle distance constraints. To address the hard constraints caused by the vehicle physical limitations and the coupled safety constraints among adjacent vehicles explicitly, the distributed model predictive control (DMPC) problem for CAVs is formulated. By virtue of the Lagrangian multiplier method and the dual decomposition technique, the DMPC problem subject to coupled constraints is recast into a distributed dual variable consensus optimization problem comprised of a series of subsystems with local copies of the dual variables, which is then cooperatively solved in parallel based on the alternating direction method of multiplier (ADMM) under the distributed information exchange mechanism. In addition, the disturbance is dynamically mitigated by the feedback control, and its influence on the vehicle status is quantified by the associated robust positively invariant set. Robust cooperative control protocols are proposed to regulate the cooperative operations of CAVs, and the recursive feasibility and the closed-loop stability are theoretically proved. Numerical experiments are carried out to illustrate the effectiveness of the proposed method.