On transmitter design in power constrained LQG control

Abstract

We consider a linear dynamic system to be controlled using feedback information that has to be transmitted over a power constrained channel with additive noise. We propose a novel approach to the transmitter design in order to minimize the cost function for the linear quadratic Gaussian (LQG) control problem when the standard state estimator and linear controller are used. We show that the well known lower bound on transmit power is tight for our solution and derive a transmission scheme that achieves this lower bound.

Optimal linear control for channels with signal-to-noise ratio constraints

“…Since then, many authors have considered similar control design problems that have been simplified by assumption of a certain controller structure, see [16], [17], [18], [19], [20]. A quite general approach was proposed in [11], but it was also noted that it leads to a difficult optimization problem with sparsity constraints when it is applied to controllers with two degrees of freedom.…”

“…Let A, B, E, F, L be given by ( 14)- (18). Application of the Youla parametrization and the Bezout identity then gives…”