Simultaneous Optimal Control and Discrete Stochastic Sensor Selection

In this paper we present the problem of combining optimal control with efficient information gathering in an uncertain environment. We assume that the decision maker has the ability to choose among a discrete set of sources of information, where the outcome of each source is stochastic. Different sources and outcomes determine a reduction of uncertainty, expressed in terms of constraints on system variables and set-points, in different directions. This paper proposes an optimizationbased decision making algorithm that simultaneously determines the best source to query and the optimal sequence of control moves, according to the minimization of the expected value of an index that weights both dynamic performance and the cost of querying. The problem is formulated using stochastic programming ideas with decision-dependent scenario trees, and a solution based on mixed-integer linear programming is presented. The results are demonstrated on a simple supply-chain management example with uncertain market demand.