J.J.P. Veerman's research was partially supported by the European Union's Seventh Framework Program (FP7-REGPOT-2012- 2013-1) under grant agreement n316165. I. Herman was supported by the Czech Science Foundation within the project GACR 13-06894S.
Wave equation, Laplacian operators, Nearest neighbor analysis (Statistics), Mathematical optimization
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.
Herman, I., Martinec, D., & Veerman, J. J. P. (2016). Transients of platoons with asymmetric and different Laplacians. Systems & Control Letters, 91, 28–35.