Dynamic Programming for Model Predictive Control of Adaptive Cruise Control Systems

This paper presents a model predictive control approach for the design of vehicular adaptive cruise control (ACC) systems by a finite horizon dynamic programming approach, which is aimed at providing automatic and steady car-following capability and enhancing riding comfort. The formalism is based on the Bellman's optimality principle and receding horizon strategy to obtain the optimal feedback control gain as evaluated by a cost function. A quadratic cost function is developed that considers the contradictions between minimal tracking error and acceleration limits of the ACC vehicle. Hence, the characteristics of permissible following distance and acceleration command are expressed as linear constraints, simultaneity. To solve the constrained finite-horizon optimal control problem, a model based optimized dynamic terminal controller is proposed to drive the system state into a terminal region as tracking error compensation. Extensive simulations and comparisons for relevant traffic scenarios of ACC systems cannot only perform to verify the proposed optimal predictive controller design but also preserve the asymptotic stability.