Simultaneous Compensation of Actuation and Communication Delays for Heterogeneous Platoons via Predictor-Feedback CACC with Integral Action

We construct a predictor-feedback cooperative adaptive cruise control (CACC) design with integral action, which achieves simultaneous compensation of long, actuation and communication delays, for platoons of heterogeneous vehicles whose dynamics are described by a third-order linear system with input delay. The key ingredients in our design are an underlying predictor-feedback law that achieves actuation delay compensation and an integral term of the difference between the delayed (by an amount equal to the respective communication delay) and current speed of the preceding vehicle. The latter, essentially, creates a virtual spacing variable, which can be regulated utilizing only delayed position and speed measurements from the preceding vehicle. We establish individual vehicle stability, string stability, and regulation for vehicular platoons, under the control design developed. The proofs rely on combining an input-output approach (in the frequency domain), with derivation of explicit solutions for the closed-loop systems, and they are enabled by the actuation and communication delays-compensating property of the design. We demonstrate numerically the control and model parameters' conditions of string stability, while we also present simulation results, in realistic scenarios, including a scenario in which the leading vehicle's trajectory is obtained from NGSIM data. All case studies confirm the effectiveness of the design developed.