本文探讨对某单一种群鱼实施捕捞作业时，在可持续捕获的条件下，捕获量最大的最优捕捞模型建立及其求解。论文在分析捕鱼过程，给出合理假设的情形下，以寻求最大捕鱼量为目标，利用微元法建立受控系统状态方程、确定了目标泛函，从而建立了捕获作业的数学模型——带约束的最优控制问题模型；进而将最优控制问题近似用一般优化模型逼近，通过Lingo软件对优化问题求解，得出最优控制问题的近似解；最后，以1996年全国大学生数学建模A题作为例子，对此问题应用我们的方法进行了求解，说明了模型的有效性。此模型可为实际生产中具体问题提供一定的借鉴和参考。
关键字：最优控制模型 捕捞强度系数 最大捕捞量
A kind of optimal control problem for fishing of establish and solution
Abstract
In this paper, optimal control problem for fishing and corresponding method of solution are introduced. We mainly consider optimal catching control problem under the case of the single species. For one hand, background of the problem is proposed and some due assumptions are given. On the basis of these hypotheses, an optimal catching control problem is established. On the other hand, we present an example from the viewpoint of application, which can be reduce to a general nonlinear optimum problem that can be resolve by mathematical Software Lingo.
key words：optimal catching control model, Solution, Mathematical Software
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