Coherent feedback that beats all measurement-based feedback protocols

TL;DR

This paper demonstrates that when control speed is limited, coherent feedback protocols can outperform all measurement-based feedback methods by utilizing geodesic paths in Hilbert space, leading to faster control.

Contribution

It introduces a minimal-time control problem showing the optimality of coherent feedback over measurement-based protocols under speed constraints.

Findings

Coherent feedback exploits geodesic paths in Hilbert space.

Coherent protocols are faster than measurement-based ones under bounded control speed.

The superiority is demonstrated in a widely applicable control problem.

Abstract

We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in a strict sense. The superiority of the coherent protocol is due to the fact that it can exploit a geodesic path in Hilbert space, a path that measurement-based protocols cannot follow.