### 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 in general unrealistic. Therefore, in this paper we consider a class of linear quantum systems subject to time-varying norm-bounded parametric uncertainty and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although the proposed observer is different from the optimal filter in the sense of the least mean square error, it is demonstrated in a typical quantum control problem that the observer is fairly robust against a parametric uncertainty even when the other estimators, the optimal Kalman filter and the risk-sensitive observer, fail in the estimation due to the uncertain perturbation.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 3138-3143 |

Number of pages | 6 |

Publication status | Published - 2006 |

Externally published | Yes |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 2006 Dec 13 → 2006 Dec 15 |

### Other

Other | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country | United States |

City | San Diego, CA |

Period | 06/12/13 → 06/12/15 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 3138-3143). [4177479]

**Robust observer for uncertain linear quantum systems.** / Yamamoto, Naoki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*, 4177479, pp. 3138-3143, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 06/12/13.

}

TY - GEN

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 in general unrealistic. Therefore, in this paper we consider a class of linear quantum systems subject to time-varying norm-bounded parametric uncertainty and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although the proposed observer is different from the optimal filter in the sense of the least mean square error, it is demonstrated in a typical quantum control problem that the observer is fairly robust against a parametric uncertainty even when the other estimators, the optimal Kalman filter and the risk-sensitive observer, fail in the estimation due to the uncertain perturbation.

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 in general unrealistic. Therefore, in this paper we consider a class of linear quantum systems subject to time-varying norm-bounded parametric uncertainty and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although the proposed observer is different from the optimal filter in the sense of the least mean square error, it is demonstrated in a typical quantum control problem that the observer is fairly robust against a parametric uncertainty even when the other estimators, the optimal Kalman filter and the risk-sensitive observer, fail in the estimation due to the uncertain perturbation.

UR - http://www.scopus.com/inward/record.url?scp=39649086667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649086667&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:39649086667

SN - 1424401712

SN - 9781424401710

SP - 3138

EP - 3143

BT - Proceedings of the IEEE Conference on Decision and Control

ER -