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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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.

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Decomposition of acceleration was investigated as an alternative to commonly used direct spectral analysis of measured acceleration or angular velocity for tremor quantification. Orientation estimation algorithm was devised to decompose the measured acceleration into inertial acceleration caused by sensor movement in inertial reference frame and gravitational artifact. Resulting signals, beside measured acceleration and angular velocity, were used to assess tremor amplitude and frequency by spectral peak detection. The algorithm was tested on experimental data from a clinical study including patients with essential tremor. Influence of sensor calibration and connections of results to analytic approach are analyzed briefly.