Section: New Results

String Stability towards Leader thanks to Asymmetric Bidirectional Controller

Participants: A. Sarlette

This result published in [21] is the result of an investigation of classical (non-quantum) distributed and coupled systems and their fundamental limitations – a sequel of A.Sarlette's previous line of work. It deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g. acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle is coupled solely to its immediate predecessor and to its immediate follower with different gains in these two directions. We show that in this setting, unlike with unidirectional or symmetric bidirectional controllers, string stability can be recovered when disturbances act only on a small (N-independent) set of leading vehicles. This improves existing results from the literature with this assumption. We also indicate that string stability with respect to arbitrarily distributed disturbances cannot be achieved with this controller.

A journal version is in preparation where we essentially close the subject, on a discrete-controller version:

- we will show that no local digital controller whatsoever (including nonlinearity, local communication,...) can achieve the academic property of string stability for infinite length chains and with bounded noise/disturbance on each member of the chain, and this implies serious consequences for practical behaviors of finite-length chains.

- conversely, we give the equivalent of the above result to show that if one is concerned mainly about the noise/disturbance acting on the leader (boundary condition of the chain), then indeed our above result achieves all existing variants of the string stability definitions.