Robust Invariant Set Design for Reliable Stopping in Adaptive Cruise Control via Model Predictive Control

Adaptive cruise control (ACC) systems are critical for ensuring safe and efficient operation in autonomous vehicles, especially in scenarios requiring precise stopping, such as approaching traffic lights or handling emergency braking. However, many existing ACC systems rely on controllers that become infeasible or fail to ensure stability in safety-critical situations, particularly under short prediction horizons and high velocity. This paper presents a novel approach that integrates invariant sets and linear quadratic regulator (LQR) into model predictive control (MPC) to address these limitations, enabling reliable stopping performance. This approach maximizes the set of recursively feasible states for the ACC compared to the current approaches. The present MPC-LQR–invariant set framework is robust under sensor noise, parameter uncertainty, and external disturbances, validating the approach for real-world scenarios. Additionally, we analyze and compare the feasibility and energy efficiency of the system for different terminal set strategies as control invariant set ( ${\mathrm {C}}_{\infty }$ ) and positive invariant set ( ${\mathrm {O}}_{\infty }$ ). The results suggest an interplay between energy efficiency and feasibility in short-horizon cases, providing actionable insights into selecting appropriate invariant set based on specific application. While control invariant set offers a larger feasible region, positive invariant set provides a more efficient energy consumption. This approach enhances ACC systems compared to previous controllers, providing safer and more reliable stopping for critical situations.