Stability Analysis of Model Predictive Control-Based Car-Following Control Under Linear Vehicle Dynamics

Abstract

The continued advancement of autonomous vehicle technologies in recent years provides a unique opportunity to correct poor traffic dynamical performance resulting from irregular human driving behavior. To this end, car-following control schemes have been designed to regulate the motions of a platoon of autonomous vehicles as an interconnected system, thereby reducing undesired congestion and oscillations in traffic flow. In the development of such algorithms, it is important to verify dynamical stability to ensure optimal control is consistently maintained. We studied a linear discrete-time dynamical system modeling the kinematics of a platoon of connected and autonomous vehicles (CAVs) driving on a straight roadway behind an uncontrolled leading vehicle. The acceleration of each CAV was treated as a control. At each discrete time step, the unique optimal solution of a general p-horizon model predictive control (MPC) optimization problem was computed to determine the next control input. We employed stability theory and matrix analysis to prove asymptotic stability of the linear closed-loop dynamics up to an MPC horizon of p=3p=3. We further used numerical methods to select appropriate penalty weights for the optimization problem to achieve desired transient and asymptotic performance. These results help illuminate and support the development of car-following MPC schemes.