Pole placement design for quantum systems via coherent observers

TL;DR

This paper develops pole-placement techniques for quantum systems using coherent observers, allowing independent design of observer and controller while respecting quantum laws, to improve quantum feedback control.

Contribution

It introduces a pole-placement method for quantum systems with coherent observers, enabling independent design and greater control flexibility in quantum feedback systems.

Findings

Pole placement for quantum systems using coherent observers is feasible.

A separation principle for quantum observer and controller design is established.

The method enhances transient response control in quantum feedback systems.

Abstract

We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-placement techniques for quantum systems using coherent observers, and in such a fashion, poles of a closed-loop quantum system can be relocated at any desired locations. In comparison to classical feedback control design incorporating the Luenberger observer, here direct coupling between a quantum plant and the observer-based controller are allowed to enable a greater degree of freedom for the design of controller parameters. A separation principle is presented, and we show how to design the observer and feedback independently to be consistent with the laws of quantum mechanics. The proposed scheme is applicable to coherent feedback control of quantum systems, especially when the transient dynamic response is of interest, and this issue is illustrated in an example.