Highlights • Develop an idealized model predictive control (MPC) strategy to coordinate the behaviors of all following connected and autonomous vehicles in a platoon. • Develop an effective solution algorithm for the embedded optimal control problem. • Derive an analytical formulation for sensitivity analysis of the optimal control problem. • Develop an analytical method for stability analysis of the idealized MPC strategy.

Abstract Recently, model predictive control (MPC)-based platooning strategies have been developed for connected and autonomous vehicles (CAVs) to enhance traffic performance by enabling cooperation among vehicles in the platoon. However, they are not deployable in practice as they require the embedded optimal control problem to be solved instantaneously, with platoon size and prediction horizon duration compounding the intractability. Ignoring the computational requirements leads to control delays that can deteriorate platoon performance and cause collisions between vehicles. To address this critical gap, this study first proposes an idealized MPC-based cooperative control strategy for CAV platooning based on the strong assumption that the problem can be solved instantaneously. It also proposes a solution algorithm for the embedded optimal control problem to maximize platoon performance. It then develops two approaches to deploy the idealized strategy, labeled the deployable MPC (DMPC) and the DMPC with first-order approximation (DMPC-FOA). The DMPC approach reserves certain amount of time before each sampling time instant to estimate the optimal control decisions. Thereby, the estimated optimal control decisions can be executed by all the following vehicles at each sampling time instant to control their behavior. However, under the DMPC approach, the estimated optimal control decisions may deviate significantly from those of the idealized MPC strategy due to prediction error of the leading vehicle's state at the sampling time instant. The DMPC-FOA approach can significantly improve the estimation performance of the DMPC approach by capturing the impacts of the prediction error of the leading vehicle's state on the optimal control decisions. An analytical method is derived for the sensitivity analysis of the optimal control decisions. Further, stability analysis is performed for the idealized MPC strategy, and a sufficient condition is derived to ensure its asymptotic stability under certain conditions. Numerical experiments illustrate that the control decisions estimated by the DMPC-FOA approach are very close to those of the idealized MPC strategy under different traffic flow scenarios. Hence, DMPC-FOA can address the issue of control delay of the idealized MPC strategy effectively and can efficiently coordinate car-following behaviors of all CAVs in the platoon to dampen traffic oscillations. Thereby, it can be applied for real-time cooperative control of a CAV platoon.