Optimal Linear Control over Channels with Signal-to-Noise Ratio Constraints
(2012) In IEEE Transactions on Automatic Control- Abstract
- We consider a networked control system where a linear time-invariant (LTI) plant, subject to a stochastic disturbance, is controlled over a communication channel with colored noise and a signal-to-noise ratio (SNR) constraint. The controller is based on output feedback and consists of an encoder that measures the plant output and transmits over the channel, and a decoder that receives the channel output and issues the control signal. The objective is to stabilize the plant and minimize a quadratic cost function, subject to the SNR constraint.
It is shown that optimal LTI controllers can be obtained by solving a convex optimization problem in the Youla parameter and performing a spectral factorization.
The... (More) - We consider a networked control system where a linear time-invariant (LTI) plant, subject to a stochastic disturbance, is controlled over a communication channel with colored noise and a signal-to-noise ratio (SNR) constraint. The controller is based on output feedback and consists of an encoder that measures the plant output and transmits over the channel, and a decoder that receives the channel output and issues the control signal. The objective is to stabilize the plant and minimize a quadratic cost function, subject to the SNR constraint.
It is shown that optimal LTI controllers can be obtained by solving a convex optimization problem in the Youla parameter and performing a spectral factorization.
The functional to minimize is a sum of two terms: the first is the cost in the classical linear quadratic control problem and the second is a new term that is induced by the channel noise.
A necessary and sufficient condition on the SNR for stabilization by an LTI controller follows directly from a constraint of the optimization problem. It is shown how the minimization can be approximated by a semidefinite program. The solution is finally illustrated by a numerical example. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2430828
- author
- Johannesson, Erik LU ; Rantzer, Anders LU and Bernhardsson, Bo LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- submitted
- subject
- keywords
- ACGN channel, control over noisy channels, linear-quadratic-Gaussian control, networked control systems, signal-to-noise ratio (SNR)
- in
- IEEE Transactions on Automatic Control
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- ISSN
- 0018-9286
- project
- LCCC
- language
- English
- LU publication?
- yes
- additional info
- Submitted to the IEEE Transactions on Automatic Control on March 30th 2012. month=March
- id
- b96f1568-2a16-4e96-be36-d929c33d9c4d (old id 2430828)
- date added to LUP
- 2016-04-04 13:54:00
- date last changed
- 2021-04-06 15:27:26
@article{b96f1568-2a16-4e96-be36-d929c33d9c4d, abstract = {{We consider a networked control system where a linear time-invariant (LTI) plant, subject to a stochastic disturbance, is controlled over a communication channel with colored noise and a signal-to-noise ratio (SNR) constraint. The controller is based on output feedback and consists of an encoder that measures the plant output and transmits over the channel, and a decoder that receives the channel output and issues the control signal. The objective is to stabilize the plant and minimize a quadratic cost function, subject to the SNR constraint. <br/><br> <br/><br> It is shown that optimal LTI controllers can be obtained by solving a convex optimization problem in the Youla parameter and performing a spectral factorization. <br/><br> The functional to minimize is a sum of two terms: the first is the cost in the classical linear quadratic control problem and the second is a new term that is induced by the channel noise.<br/><br> <br/><br> A necessary and sufficient condition on the SNR for stabilization by an LTI controller follows directly from a constraint of the optimization problem. It is shown how the minimization can be approximated by a semidefinite program. The solution is finally illustrated by a numerical example.}}, author = {{Johannesson, Erik and Rantzer, Anders and Bernhardsson, Bo}}, issn = {{0018-9286}}, keywords = {{ACGN channel; control over noisy channels; linear-quadratic-Gaussian control; networked control systems; signal-to-noise ratio (SNR)}}, language = {{eng}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Automatic Control}}, title = {{Optimal Linear Control over Channels with Signal-to-Noise Ratio Constraints}}, url = {{https://lup.lub.lu.se/search/files/6231875/2430829.pdf}}, year = {{2012}}, }