On LQG control with communication power constraint

We study the problem of LQG control under communication power constraints by naturally extending the LQG cost to include a penalty for communication power. Our problem formulation is inspired by classical LQG control and optimal sensor selection. We study the computational complexity of the resulting optimization by examining its convexity. Although in high dimensional systems, the optimization problem is not known to be convex, we show that the special case of unstable scalar systems yields a convex optimization problem.