Robustness of String Stability of Linear Predictor-Feedback CACC to Communication Delay

Linear predictor-feedback Cooperative Adaptive Cruise Control (CACC) achieves actuator delay compensation in vehicular platoons, provided that there is no vehicle-to-vehicle (V2V) communication delay. In the present paper we establish robustness of string stability of predictor-feedback CACC to (uncertain) communication delay. The robustness property is established for heterogeneous vehicular platoons, in which, each individual vehicle's dynamics are described by a third-order linear system with input delay. The proof of robustness relies on employment of an input-output approach in the frequency domain, which enables derivation of explicit conditions on the value of communication delay, which guarantee string stability, depending on control laws and vehicle models parameters. The theoretical guarantees of string stability and the respective conditions on parameters are thoroughly illustrated also numerically.