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

Summary, in English

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.

• Author: Erik Johannesson; Anders Rantzer; Bo Bernhardsson
• Department/s: Department of Automatic Control; ELLIIT: the Linköping-Lund initiative on IT and mobile communication
• Publishing year: 2012
• Language: English
• Publication/Series: IEEE Transactions on Automatic Control
• Full text: - 194 kB; Download statistics
• Document type: Journal article
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Control Engineering
• Keywords: ACGN channel; control over noisy channels; linear-quadratic-Gaussian control; networked control systems; signal-to-noise ratio (SNR)
• Status: Submitted
• Project: LCCC
• Research group: LCCC
• ISBN/ISSN/Other: ISSN: 0018-9286