Sensitivity Function Trade-offs for Networks with a String Topology

TL;DR

This paper investigates the fundamental trade-offs in sensitivity functions for networks with string topology, revealing how network growth influences regulation and stability, especially in vehicle platoons.

Contribution

It introduces two sensitivity function trade-offs specific to string topology networks, linking network growth to regulation limitations and stability issues.

Findings

Lower bounds on H-infinity norm established

Bode sensitivity relations derived for network families

Explains poor regulation in long vehicle platoons

Abstract

We present two sensitivity function trade-offs that apply to a class of networks with a string topology. In particular we show that a lower bound on the H-infinity norm and a Bode sensitivity relation hold for an entire family of sensitivity functions associated with growing the network. The trade-offs we identify are a direct consequence of growing the network, and can be used to explain why poorly regulated low frequency behaviours emerge in long vehicle platoons even when using dynamic feedback.