研究在周期环境下由Gompertz模型描述的种群系统的优化收获控制问题.在给定时刻对种群进行脉冲收获,在系统保持周期变化的前提下,考虑收获成本因素,以最大经济净收益为目标,研究收获努力量对收益的影响并确定最优的收获控制策略.首先证明了最优控制策略的存在性,进一步利用脉冲微分系统的极值原理,获得了最优解满足的数值方程组.并在两种特殊情况下得到了满足一定条件的最优解.该结果推广和改进了现有文献的一些结果.

In this paper, we consider the optimal harvesting control of a biological species system whose growth is governed by the Gompertz equation with periodic
coefficients. The species is harvested at fixed moments for economic profit. 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 linearly on the control variable. The existence of an optimal impulsive harvest control is proven, and by the maximum principle for optimal impulse control  problem, and the optimal control is characteriged by using the optimality system. Two special cases are considered, and the  precise optimal controls are achieved for the two cases.