Optimal Impulsive Control Strategy of Forest Ecosystem Sustainable Development

In this paper, we consider the optimal harvesting control of a forest ecosystem whose growth is governed by the Gompertz equation, the species in the forest is harvested at fixed moments for economic profit. In order to ensure sustainable development, we mainly concern the optimal periodic control strategy. The purpose is to control the harvesting effort so as to maximize the profit which is the difference between economic revenue and cost, assuming that the cost in the payoff functional depends quadratically on the control variable. We show the existence of a periodic optimal impulsive harvest control, and under certain condition, we characterize the optimal control in terms of a periodic impulsive optimality system.