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

TL;DR

This paper develops a convex optimization framework to design optimal linear controllers for networked control systems with SNR constraints, accounting for colored noise and channel noise effects.

Contribution

It introduces a method to obtain optimal LTI controllers via convex optimization in the Youla parameter, considering channel noise and SNR constraints.

Findings

Optimal controllers derived from convex optimization and spectral factorization.

Necessary and sufficient SNR conditions for stabilization.

Approximation of the solution via semidefinite programming.

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 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. %todo ta bort meningen? 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.