Control of sensors of a Gaussian stochastic control system

With which intensity to request high-quality components of the observed output of a Gaussian system driven by Brownian motions so as to minimize the trace of the error covariance when there is a cost for doing so? The optimal stochastic control problem is considered on an infinite horizon and with a discounted cost, and separately also for discounted impulse control. The optimal control law is for the scalar cases proven to be a threshold control law. The dynamic behavior of the closed-loop system is such that if the conditional variance is large then the sensor input for better quality observations is switched on while if the uncertainty is small then the input for better quality observations is switched off. The optimal control law for the drift input is identical to the classical LQG case.