We study a model for the exploitation of renewable stocks developed in Clark et al. (Econometrica 47 (1979), 25-47). In this particular control problem, the control law contains a measurable and an impulsive control component. We formulate Pontryagin's maximum principle for this kind of control problems, proving first order necessary conditions of optimality. Manipulating the correspondent Lagrange multipliers we are able to define two special switch functions, that allow us to describe the optimal trajectories and control policies nearly completely for all possible initial conditions in the phase plane.

翻译：我们研究了克拉克等人开发的开发可再生种群的模式(Econoricta 47(1979), 25-47),在这一具体的控制问题中,控制法包含一个可测量和冲动控制部分,我们为这种控制问题制定了Pontryagin的最大原则,证明第一阶必要的最佳条件。我们操纵了相应的拉格朗格乘数,可以确定两个特殊的开关功能,使我们能够对阶段平面上所有可能的初始条件几乎完全描述最佳轨迹和控制政策。