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Optimal Linear Control over Channels with Signal-to-Noise Ratio Constraints

Johannesson, Erik LU ; Rantzer, Anders LU and Bernhardsson, Bo LU (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)
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author
organization
publishing date
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
id
b96f1568-2a16-4e96-be36-d929c33d9c4d (old id 2430828)
date added to LUP
2012-04-02 15:22:32
date last changed
2016-04-16 11:49:31
@misc{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},
  keyword      = {ACGN channel,control over noisy channels,linear-quadratic-Gaussian control,networked control systems,signal-to-noise ratio (SNR)},
  language     = {eng},
  publisher    = {ARRAY(0xa3c9268)},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Optimal Linear Control over Channels with Signal-to-Noise Ratio Constraints},
  year         = {2012},
}