Platoon-centered control for eco-driving at signalized intersection built upon hybrid MPC system, online learning and distributed optimization part II: Theoretical analysis

Extensive studies developed eco-driving strategies to smooth traffic and reduce energy consumption and emission at signalized intersections. Part I (Zhang and Du, 2022) of this study developed a novel platoon-centered control for eco-driving (PCC-eDriving), considering a mixed flow involving Connected and Autonomous Vehicles (CAVs) and Human-Driven Vehicles (HDVs). This PCC-eDriving is mathematically implemented by a hybrid Model Predictive Control (MPC) system and solved by an active-set based optimal condition decomposition algorithm (AS-OCD). It generates discrete control laws for a platoon to approach, split as sub-platoons as needed, and then pass the intersections smoothly and efficiently. Though the numerical experiments validated the effectiveness, the theoretical properties of the hybrid MPC system and the solution algorithms were not investigated. Part II of this study thus focused on these theoretical analyses. Mainly, we first analyzed and proved the MPC sequential feasibility and hybrid system switching feasibility to guarantee the control continuity of the hybrid MPC system. Next, we factored CAV control uncertainties and proved the Input-to-state stability of the robust MPC controller. These proofs theoretically ensured the effectiveness and robustness of the hybrid MPC system. Last, we proved the solution optimality and convergence of the AS-OCD algorithm. It confirmed that the AS-OCD algorithm could find the global optimal solutions for the MPC optimizers with a linear convergence rate.