Steering state statistics with output feedback

Yongxin Chen; Tryphon Georgiou; Michele Pavon

doi:10.1109/CDC.2015.7403244

Steering state statistics with output feedback

Yongxin Chen, Tryphon Georgiou, Michele Pavon

Electrical and Computer Engineering

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

8 Scopus citations

Abstract

Consider a linear stochastic system whose initial state is a random vector with a specified Gaussian distribution. Such a distribution may represent a collection of particles abiding by the specified system dynamics. In recent publications, we have shown that, provided the system is controllable, it is always possible to steer the state covariance to any specified terminal Gaussian distribution using state feedback. The purpose of the present work is to show that, in the case where only partial state observation is available, a necessary and sufficient condition for being able to steer the system to a specified terminal Gaussian distribution for the state vector is that the terminal state covariance be greater (in the positive-definite sense) than the error covariance of a corresponding Kalman filter.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6502-6507
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7403244
State	Published - Feb 8 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	12/15/15 → 12/18/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

Kalman filter
Linear stochastic systems
covariance control
stochastic control

Publisher link

10.1109/CDC.2015.7403244

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Chen, Y., Georgiou, T., & Pavon, M. (2015). Steering state statistics with output feedback. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 6502-6507). [7403244] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403244

Steering state statistics with output feedback. / Chen, Yongxin; Georgiou, Tryphon; Pavon, Michele.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 6502-6507 7403244 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

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

Chen, Y, Georgiou, T & Pavon, M 2015, Steering state statistics with output feedback. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7403244, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 6502-6507, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7403244

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abstract = "Consider a linear stochastic system whose initial state is a random vector with a specified Gaussian distribution. Such a distribution may represent a collection of particles abiding by the specified system dynamics. In recent publications, we have shown that, provided the system is controllable, it is always possible to steer the state covariance to any specified terminal Gaussian distribution using state feedback. The purpose of the present work is to show that, in the case where only partial state observation is available, a necessary and sufficient condition for being able to steer the system to a specified terminal Gaussian distribution for the state vector is that the terminal state covariance be greater (in the positive-definite sense) than the error covariance of a corresponding Kalman filter.",

keywords = "Kalman filter, Linear stochastic systems, covariance control, stochastic control",

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AU - Georgiou, Tryphon

AU - Pavon, Michele

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N2 - Consider a linear stochastic system whose initial state is a random vector with a specified Gaussian distribution. Such a distribution may represent a collection of particles abiding by the specified system dynamics. In recent publications, we have shown that, provided the system is controllable, it is always possible to steer the state covariance to any specified terminal Gaussian distribution using state feedback. The purpose of the present work is to show that, in the case where only partial state observation is available, a necessary and sufficient condition for being able to steer the system to a specified terminal Gaussian distribution for the state vector is that the terminal state covariance be greater (in the positive-definite sense) than the error covariance of a corresponding Kalman filter.

AB - Consider a linear stochastic system whose initial state is a random vector with a specified Gaussian distribution. Such a distribution may represent a collection of particles abiding by the specified system dynamics. In recent publications, we have shown that, provided the system is controllable, it is always possible to steer the state covariance to any specified terminal Gaussian distribution using state feedback. The purpose of the present work is to show that, in the case where only partial state observation is available, a necessary and sufficient condition for being able to steer the system to a specified terminal Gaussian distribution for the state vector is that the terminal state covariance be greater (in the positive-definite sense) than the error covariance of a corresponding Kalman filter.

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Steering state statistics with output feedback

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