This talk will have two main parts: transfer functions in directed graphs with higher order dynamics and applications of these results to platooning. Both parts deal with identical agents with possibly higher-order dynamics. In the first part a simple product form of the transfer function between controlling agents and observing agent is introduced and derived. Although the location of poles in transfer functions in graph is well known, the location of zeros received low attention. Additionally, some relations to the graph topology with nice algebraic properties is shown.
The second part deals with scaling properties of bidirectional vehicular platoons. Partially using the results on the transfer functions, we prove that whenever asymmetry in the platoon is present, the Hinf norm of the system must grow exponentially. By asymmetry we mean stronger effect of spacing error in the direction towards the platoon leader. In addition, a new approach for transient time improvement in symmetric platoons will be presented. It is based on "wave absorbtion" at the leader. This kind of control allows only linear scaling of transient time with the number of vehicles. The absorption is based on theoretically interesting "wave transfer function", which is also introduced.
Ivo is a doctoral student supervised by Michael Šebek since September 2012. He got his Ing. (MSc) degree at Brno University of Technology in 2012 for his work on sensorless control of electric motors supervised by Pavel Václavek. Ivo's doctoral research is focused on control theory for distributed and networked systems.