Motivated by area coverage optimization problems with time-varying risk densities, in this paper we propose a decentralized control law for a team of autonomous mobile agents in a 2-D area such that their asymptotic configurations optimize a generalized non-autonomous coverage metric. We emphasize that the generalized non-autonomous coverage metric explicitly depends on a nonuniform time-varying measurable scalar field that is defined by the trajectories of a set of mobile targets (distinct from the agents). The time-varying density that we consider here is not directly controllable by agents. We show that under certain conditions on the density defined on a closed bounded region of operation, the agents configure themselves asymptotically to optimize a related generalized non-autonomous coverage metric. A set of simulations illustrates the proposed control. (C) 2017 Elsevier Ltd. All rights reserved.