Adaptive Cruise Control Design Using Reach Control

We investigate a correct-by-construction synthesis of piecewise affine feedback controllers designed to satisfy the strict safety specifications set forth by the adaptive cruise control (ACC) problem. Our design methodology is based on the formulation of the ACC problem as a reach control problem on a polytope in a 2D state space. The boundaries of this polytope, expressed as linear constraints on the states, arise from the headway and velocity safety requirements imposed by the ACC problem statement. We propose a model for the ACC problem, develop a controller that satisfies the ACC requirements, and produce simulations for the closed-loop system.