A simplified stochastic optimization model for logistic dynamics with control-dependent carrying capacity
A simplified stochastic optimization model for logistic dynamics with control-dependent carrying capacity
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DOI：
10.1080/17513758.2019.1576927
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发表时间：
2019-01-01
影响因子：
2.8
通讯作者：
Yoshioka, Hidekazu
中科院分区：
文献类型：
--
作者：
Yoshioka, Hidekazu
针对河流环境中藻类种群管理问题，提出了一种简化的随机控制模型，用于优化具有控制依赖承载能力的物流动力学。求解优化问题归结为求解一个非局部一阶微分方程，称为tt-Jacobi-Bellman（HJB）方程。结果表明，HJB方程具有唯一的粘性解，该解可以用有限差分格式近似。的解决方案和最优控制的渐近估计，并与数值解相比。最后，最优控制的参数依赖性进行了数值研究与河流环境管理的影响。
A simplified stochastic control model for optimization of logistic dynamics with the control-dependent carrying capacity, which is motivated by a recent algae population management problem in the river environment, is presented. Solving the optimization problem reduces to finding a solution to a non-local first-order differential equation called tt-Jacobi-Bellman (HJB) equation. It is shown that the HJB equation has a unique viscosity solution and that the solution can be approximated with a finite difference scheme. Asymptotic estimates of the solution and the optimal control are derived and compared with numerical solutions. Finally, parameter dependence of the optimal control is examined numerically with implications to river environmental management.