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

Publiceringsår: 2012
Språk: Engelska
Publikation/Tidskrift/Serie: IEEE Transactions on Automatic Control
Dokumenttyp: Artikel
Ytterligare information: Submitted to the IEEE Transactions on Automatic Control on March 30th 2012. month=March


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.



  • Technology and Engineering
  • ACGN channel
  • control over noisy channels
  • linear-quadratic-Gaussian control
  • networked control systems
  • signal-to-noise ratio (SNR)


  • Vetenskapsrådet
  • LCCC
  • LCCC
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