环境污染下一类具有尺度结构种群系统的最优控制

Optimal Control of a Size-Structured System in a Polluted Environment

摘要: 本文首次研究了环境污染下一类具有尺度结构的种群系统的最优控制问题，通过控制种群的收获和外界毒素向环境的输入率使得人们的总收益最大。利用不动点定理得到了系统解的存在唯一性，借助法锥切锥理论结合共轭系统的技巧推导了收获控制为最优的必要条件，从而推广了一些文献中的已有结果。

Abstract: In this paper, we investigate the optimal harvesting for a class of size-structured population system in a polluted environment, making the maximum revenue by controlling the species harvest and inputting rates of the external toxin into the environment. Fixed point theory is used to obtain the existence and uniqueness of solution of the system. Optimality conditions are derived by means of tangent-normal cones and the technique of adjoint system. Some results in references are extended.