Transients of platoons with asymmetric and different Laplacians

Abstract

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

Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling

“…A good scaling of system norms with such an approach was numerically shown in [10] and the properties of the platoon's response to a step change in leader's velocity were derived in [6]. Using these properties, the parameters of the controller as well as the coefficient of asymmetry can be optimised to minimise the transient time [13]. In both papers [6,13] it was shown that symmetry in position is necessary for a good scaling.…”

“…Using these properties, the parameters of the controller as well as the coefficient of asymmetry can be optimised to minimise the transient time [13]. In both papers [6,13] it was shown that symmetry in position is necessary for a good scaling. In addition, it was proved in [20] that symmetry in position is a necessary condition for "local" string stability.…”

“…To the best knowledge of the authors, this is the first paper which analytically proves better scaling when symmetry in position and asymmetry in velocity is used. The papers[6,13] relied in their proofs only on (reasonable, though) conjectures.…”

Dynamics of Locally Coupled Agents with Next Nearest Neighbor Interaction

“…The Routh-Hurwitz criterion is a standard strategy to derive a concise set of conditions that is equivalent to the condition that all roots of a given polynomial have negative real parts. In various systems similar to the ones discussed here, this criterion gives good results [20,9]. In our current case the resulting equations are too complicated to give us much information and we only get one more necessary condition for stability that we can use, namely Corollary 6.1.…”

“…In doing this one needs to be aware though that (i) assumptions or conjectures needed to solve the old problem must be investigated again as they may not be justified anymore, and (ii) new phenomena may arise. For more details see [20,21,9].…”