Robust String Stability and Safety of CTH Predictor-Feedback CACC

Abstract

We establish robustness of string stability to delay uncertainty as well as positivity of spacing and speed states, for homogeneous vehicular platoons under predictor-feedback Cooperative Adaptive Cruise Control (CACC). Each individual vehicle’s dynamics are described by a second-order linear system with delayed desired acceleration, under acceleration information transmitted to the ego vehicle from a single, preceding vehicle. The nominal design (in the delay-free case) is a constant time-headway (CTH) policy and no restriction on the delay size, in relation with the desired time headway, is imposed. The proofs rely on combination of an input-output approach (on the frequency domain) and on deriving estimates on explicit, closed-loop solutions; under specific, sufficient conditions that are derived on initial conditions and parameters of the baseline, CTH controller. We illustrate in simulation and numerical examples, the guarantees of robust stability and string stability as well as of collisions avoidance, of CTH predictor-feedback CACC design. We also present extensions of our design and analysis approach to heterogeneous, third-order dynamic models of vehicles.