Motivated by area coverage optimization problems with time varying risk densities, we propose a decentralized control law for a team of autonomous mobile agents in a two dimensional area such that their asymptotic configurations optimize a generalized non-autonomous coverage metric. The generalized non-autonomous coverage metric explicitly depends on a nonuniform time-varying measurable scalar field that is not directly controllable by agents. Several interesting scenarios emerge with time varying risk density. In this work, we consider the case of area surveillance against moving targets or external threats penetrating through the perimeter, and the case of environmental monitoring and intervention with deployment of mobile sensors in areas affected by penetration of substances governed by diffusion mechanisms, as for example oil in a marine environment. In the presence of time-varying risk density the coverage metric is non-autonomous as it includes a time varying component that does not depend on the evolution of the agents. Our non-autonomous feedback law accounts for the time-varying component through a term that vanishes when the risk eventually stops evolving. Optimality with respect to the induced non-autonomous coverage is proven in the framework of Barbalat’s lemma, and the performance is illustrated through simulation of the these two scenarios.

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