Among the various applications for fleets of UAVs, searching and tracking mobile targets remains a challenging task. In this paper, a distributed set-membership estimation and control scheme is presented. This scheme relies on the description of uncertainty and noise as bounded processes. Constraints on the field of view, as well as the presence of false targets, are taken into account. Each UAV maintains several set estimates: one for each detected and identified true target, one for detected but not yet identified targets, and one for not yet detected targets, which is also the subset of the state space still to be explored. These sets are updated by each UAV using the information coming from its sensors as well as received from its neighbors. A distributed set-membership model predictive control approach is considered to compute the trajectories of UAVs. The control input minimizing a measure of the volume of the set-membership estimates predicted h-step ahead is then evaluated. Simulations of scenarios including the presence of false targets illustrate the ability of the proposed approach to efficiently search and track an unknown number of moving targets within some delimited search area.