Numerical computation of the optimal vector field in a fishery model
Numerical computation of the optimal vector field in a fishery model
复制标题
渔业模型中最优矢量场的数值计算
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
D. Grass
中科院分区：
文献类型：
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作者：
D. Grass
经济学中分析的许多最优控制模型都被描述为折扣无限时间范围问题，其中发生函数在状态中和在控制中一样是非线性的。因此，解决方案往往只能从数字上找到。此外，长期最优解在压倒性的情况下是极限集，如均衡和/或极限环。利用这些“平凡”解，用边界元方法和延拓技术计算了最优矢量场的参数依赖的动力学结构。我们使用一个一维渔业最优控制模型来举例说明数值技术。但这些方法，如将显示的，适用于具有任意数量的状态变量和控制变量的更广泛类别的最优控制问题。
Many of the optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the occurring functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are in the overwhelming cases limit sets like equilibria and/or limit cycles. Using these “trivial” solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one-dimensional optimal control model of fishery to exemplify the numerical techniques. But these methods, as will be shown, are applicable to a much wider class of optimal control problems with any number of state and control variables.