We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix-the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H∞ norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.Index Terms-Vehicular platoons, Fiedler eigenvalue, harmonic instability, eigenvalues uniformly bounded from zero, asymmetric control, exponential scaling.

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We consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is string unstable. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.

We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, an optimization-based procedure is used to find the controller properties

The paper tailors the so-called wave-based control popular in the field of flexible mechanical structures to the field of distributed control of vehicular platoons. The proposed solution augments the symmetric bidirectional control algorithm with a wave-absorbing controller implemented on the leader, and/or on the rear-end vehicle. The wave-absorbing controller actively absorbs an incoming wave of positional changes in the platoon and thus prevents oscillations of inter-vehicle distances. The proposed controller significantly improves the performance of platoon manoeuvrers such as acceleration/deceleration or changing the distances between vehicles without making the platoon string unstable. Numerical simulations show that the wave-absorbing controller performs efficiently even for platoons with a large number of vehicles, for which other platooning algorithms are inefficient or require wireless communication between vehicles.