Optimal Impulse Control for Periodic Gompertz Systems

This article considers the optimal harvesting control of a biological species system of which the growth is governed by the periodic Gompertz system. The species is harvested at fixed moments, and the optimal control criterion is to maximize the profit which is the difference between economic revenue and cost. We assume that the cost depends quadratically on the control variable. Using the maximum principle for optimal impulse control problem, under certain assumptions, we characterize the optimal control in terms of an impulsive optimality system.