Nonlinear predictor-feedback cooperative adaptive cruise control of vehicles with nonlinear dynamics and input delay

We construct a nonlinear predictor-feedback cooperative adaptive cruise control (CACC) design for homogeneous vehicular platoons subject to actuators delays, which achieves: (i) positivity of vehicles' speed and spacing states, (ii) Script capital L infinity$$ {\mathcal{L}}_{\infty } $$ string stability of the platoon, (iii) stability of each individual vehicular system, and (iv) regulation to the desired reference speed (dictated by the leading vehicle) and spacing. The design relies on a nominal, nonlinear adaptive cruise control (ACC) law that we construct, which guarantees (i)-(iv) in the absence of actuator delay, and nonlinear predictor feedback. We consider a classical (for ACC/CACC design) third-order, nonlinear model subject to input delay, for the vehicles' dynamics. The proofs of the theoretical guarantees (i)-(iv) rely on derivation of explicit estimates on solutions (both during open-loop and closed-loop operation), capitalizing on the ability of predictor feedback to guarantee complete delay compensation after the dead-time interval has elapsed, and derivation of explicit conditions on initial conditions and parameters of the nominal control law. We also present consistent simulation results, considering a platoon of ten vehicles, which validate the design developed.