Optimal Control of Harvesting of a Distributed Renewable Resource on the Earth’s Surface

This paper is devoted to the optimal control of mixed (stationary and periodic impulse) harvesting of a renewable resource distributed on the Earth’s surface. Examples of such a resource are biological populations, including viruses, chemical contaminants, dust particles, and the like. It is proved that on an infinite planning horizon, there exists an admissible control ensuring the maximum of time-averaged harvesting.