This paper considers a string of vehicles where the local control law uses the states of the vehicle’s immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen dierent to the coupling towards the following vehicle, which is often referred to as an asymmetric bidirectional string. Further, the coupling dierences, i.e., asymmetry, can be chosen dierently for the velocity and the position coupling between neighbouring vehicles. This general approach includes the special cases of symmetric bidirectional strings and predecessor following control schemes. It is investigated how the eect of disturbance on the control errors in the string changes with the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interaction in both states, i.e., in symmetric bidirectional strings, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improves the performance of the string. Extensive numerical results illustrating the theoretical findings are also presented.

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