In this investigation, an optimal control problem for a stochastic mathematical model of population competition is studied. We have considered the stochastic model of population competition by adding the stochastic terms to the deterministic model to take into account the random perturbations and uncertainties caused by the environment to have more reliable model. The model has formulated the population densities competing against each other to be saved from destruction, attract more members and so on, using two nonlinear stochastic parabolic equations. Four factors including the status and the growth rates of the populations are considered as the control variables (which can be controlled by the members of the populations or policy makers who make decisions for the populations for particular purposes) to control the evolution of the population densities. Then, the optimal control problem for the stochastic model of population competition is studied. Employing the tangent-normal cone techniques, the Ekeland variational principle and other theorems proved throughout the paper, we have shown there exists unique stochastic optimal control. We have also presented the exact form of the optimal control in terms of stochastic adjoint states.

在这项调查中，研究了人口竞争随机数学模型的最优控制问题。我们通过在确定性模型中加入随机项来考虑人口竞争的随机模型，以考虑环境引起的随机扰动和不确定性，从而具有更可靠的模型。该模型使用两个非线性随机抛物线方程制定了相互竞争的人口密度，以防止破坏，吸引更多成员等。将人口状况和人口增长率等四个因素作为控制变量（可由人口成员或为特定目的为人口做出决策的决策者控制）来控制人口密度的演变. 然后，研究了人口竞争随机模型的最优控制问题。采用切线法向锥技术、Ekeland变分原理和整篇论文证明的其他定理，我们证明了存在独特的随机最优控制。我们还根据随机伴随状态提出了最优控制的确切形式。Ekeland 变分原理和其他定理证明了整篇论文，我们已经证明存在唯一的随机最优控制。我们还根据随机伴随状态提出了最优控制的确切形式。Ekeland 变分原理和其他定理证明了整篇论文，我们已经证明存在唯一的随机最优控制。我们还根据随机伴随状态提出了最优控制的确切形式。