Abstract
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators-the optimal Kalman filter and risk-sensitive observer-fail in the estimation.
| Original language | English |
|---|---|
| Article number | 032107 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 74 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2006 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
Cite this
Robust observer for uncertain linear quantum systems. / Yamamoto, Naoki.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 74, No. 3, 032107, 2006.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Robust observer for uncertain linear quantum systems
AU - Yamamoto, Naoki
PY - 2006
Y1 - 2006
N2 - In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators-the optimal Kalman filter and risk-sensitive observer-fail in the estimation.
AB - In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators-the optimal Kalman filter and risk-sensitive observer-fail in the estimation.
UR - http://www.scopus.com/inward/record.url?scp=33748975146&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33748975146&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.74.032107
DO - 10.1103/PhysRevA.74.032107
M3 - Article
AN - SCOPUS:33748975146
VL - 74
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 3
M1 - 032107
ER -