In multi-object stochastic systems, the issue of sensor management is a theoretically and computationally challenging problem. In this paper, we present a novel random finite set (RFS) approach to the multi-target sensor management problem within the partially observed Markov decision process (POMDP) framework. The multi-target state is modelled as a multi-Bernoulli RFS, and the multi-Bernoulli filter is used in conjunction with two different control objectives: maximizing the expected Renyi divergence between the predicted and updated densities, and minimizing the expected posterior cardinality variance. Numerical studies are presented in two scenarios where a mobile sensor tracks five moving targets with different levels of observability. Crown Copyright (C) 2014 Published by Elsevier Ltd. All rights reserved.