This paper studies the stability and scalability of the platoon where multiple vehicles move in a closed roadway and are coupled in a bidirectional ring. Each vehicle regulates its longitudinal motion based on bidirectional asymmetric control with triple asymmetry factors. By exploiting Hermite stability criterion, we derive necessary and sufficient conditions of stability for the n-vehicle platoon. Based on parametric robustness analysis, necessary and sufficient conditions of scalably asymptotic stability are further obtained, meaning that the stability is independent of the number of vehicles in the platoon. It is proved that symmetric spacing feedback is necessary for scalably asymptotic stability and the first spatial mode is the least stable among all the non-zero modes. Numerical computations show that the stability region in the space of feedback gains is favourable when the asymmetry level on speed gain is small and the asymmetry level on acceleration gain is large, whereas it may deteriorate rapidly when these two asymmetry factors have different signs.

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This paper investigates the local and global performance of the platoon where multiple identical vehicles move in a closed roadway and cooperate based on nearest-neighbour interactions. The information from the front neighbour, namely position, speed, and acceleration, is weighted non-equally component-wise to that from the back neighbour, which is quantified by the asymmetry level on each component. The local performance refers to the locally propagating attenuation for the bidirectional control, which captures whether the disturbance is amplified when propagating from a vehicle to its immediate neighbours. The global performance refers to the system transfer scalability, which characterises the scalability of system transfer matrix. Based on forward and backward wave transfer functions, several analytical necessary conditions of the locally propagating attenuation are obtained. Furthermore, two of these necessary conditions happen to be the same with the conditions for scalably asymptotic stability. Under mild assumptions, the locally propagating attenuation is sufficient for scalably asymptotic stability, the latter of which in turn implies the system transfer scalability. Numerical calculations further show that it is favourable for both performance measures to select the asymmetry levels on speed and acceleration with small magnitudes and located around the centre line of the band-like region of scalably asymptotic stability.

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