On the necessity of symmetric positional coupling for string stability

TL;DR

This paper demonstrates that in distributed systems with identical agents and asymmetric control, symmetric positional coupling is necessary for string stability, especially when agents have two integrators, using a wave transfer function approach.

Contribution

It establishes the necessity of symmetric positional coupling for string stability in systems with asymmetric bidirectional control and complex controller asymmetries.

Findings

Symmetric positional coupling is required for string stability with two integrators.

Wave transfer function approach effectively analyzes complex controller asymmetries.

Asymmetry in controllers can be tolerated if positional coupling remains symmetric.

Abstract

We consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is locally string unstable. This finding holds also for a distributed system with a generalized path-graph interaction topology due to the local nature of the wave transfer function. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.