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# Scaling in vehicle platoons[edit]

**Author**: Ivo Herman

This thesis deals with analysis of scaling in autonomous vehicle platoons in which vehicles keep fixed distance to their neighbors. The vehicles are modelled as linear single-input single-output systems of arbitrary order. In order to control themselves, the vehicles use information from their nearest neighbors - their predecessor and successor. The states used for coupling are mainly position and velocity, but other states are allowed too. The errors to neighbors in these states can be weighted differently, hence the control law is asymmetric. Using the tools from distributed control, properties of platoons are analyzed. A comprehensive overview of the properties of platoons when identical asymmetry in all states is given. With the help of a newly derived product form of a transfer function in a network system, the steady-state gain, stability, string stability and particularly H-infinity norms are analyzed. The most important aspect specifying the scaling rate is the number of integrators in the open loop. For one integrator in the open loop the scaling of the H-infinity norm is quadratic for symmetric control and linear for asymmetric control. For two and more integrators the scaling is cubical for symmetric control and exponential for asymmetric. Since there is no good control for two integrators in the open loop with identical asymmetry, symmetric coupling in position and asymmetric in velocity is proposed. Such control is, at least for the cases analyzed in the thesis, superior to both completely symmetric and completely asymmetric control. It has similar convergence time as asymmetric control but it still keeps the bounded control effort as the symmetric control does.

**Ivo Herman**, mailto:ivo.herman@fel.cvut.cz