Optimal multi-vehicle adaptive search with entropy objectives

The problem of searching for an unknown object occurs in important applications, ranging from security, medicine and defense. Modern sensors have significant processing capabilities that allow for in situ processing and exploitation of the information to select what additional information to collect. In this paper, we discuss a class of dynamic, adaptive search problems involving multiple sensors sensing for a single stationary object, and formulate them as stochastic control problems with imperfect information. The objective of these problems is related to information entropy. This allows for a complete characterization of the optimal strategies and the optimal cost for the resulting finite-horizon stochastic control problems. We show that the computation of optimal policies can be reduced to solving a finite number of strictly concave maximization problems. We further show that the solution can be decoupled into a finite number of scalar concave maximization problems. We illustrate our results with experiments using multiple sensors searching for a single object.