Scaling of transfer functions in vehicular platoons: the role of asymmetry disputed

This paper investigates disturbance propagation in vehicular platoons. In particular, we investigate how the H- infinity norm of some chosen transfer functions scale with the number of vehicles in the platoon. Dependency on the number of integrators in open-loop transfer functions is also investigated. The transfer functions are presented in a new and convenient product form. A simple test for bidirectional string stability is presented as well as conditions for undesired exponential scaling in the frequency domain. Although some recent results in communication-free vehicular platooning suggest that introducing asymmetry between the front and the rear spacing is beneficial for scaling, we show that there are actually only a few cases when asymmetry can help. It either scales badly in the H-infinity norm or is outperformed by the predecessor following control scheme. The distinction is based on number of integrators in the open loop. Index Terms—Vehicular platoons, string stability, harmonic instability, eigenvalues uniformly bounded from zero, asymmetric control.