Optimal Sensor Querying: General Markovian and LQG Models With Controlled Observations

This paper is motivated by networked control systems deployed in a large-scale sensor network where data collection from all sensors is prohibitive. We model it as a class of discrete-time stochastic control systems for which the observations available to the controller are not fixed, but there are a number of options to choose from, and each choice has a cost associated with it. The observation costs are added to the running cost of the optimization criterion and the resulting optimal control problem is investigated. Since only part of the observations are available at each time step, the controller has to balance the system performance with the penalty of the requested information (query). We first formulate the problem for a general partially observed Markov decision process model and then specialize to the stochastic linear quadratic Gaussian problem. We focus primarily on the ergodic control problem and analyze this in detail.