论文标题
非线性随机抛物线竞争模型的最佳控制
Optimal Control for a Nonlinear Stochastic Parabolic Model of Language Competition
论文作者
论文摘要
在这项调查中，研究了语言竞争的随机数学模型的最佳控制问题。我们通过将随机术语添加到确定性模型中，以考虑环境引起的随机扰动和不确定性，以考虑到具有更可靠的模型的随机扰动和不确定性，从而考虑了语言竞争的随机模型。该模型已经制定了两种语言的说话者的人口密度，这些语言互相竞争，以免被摧毁，吸引更多的演讲者，依此类推，依此类推，使用两个非线性随机抛物线方程。包括语言状态和人口的增长率在内的四个因素被认为是控制变量（可以由人口的说话者或为特定目的做出决定的人群的说话者控制），以控制人口密度的演变。然后，研究了语言竞争随机模型的最佳控制问题。在整个论文中，Ekeland差异原理和其他定理采用了切线正常锥技术，我们已经证明存在独特的随机最佳控制。我们还根据随机伴随状态介绍了最佳控制的确切形式。
In this investigation, an optimal control problem for a stochastic mathematical model of language competition is studied. We have considered the stochastic model of language 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 of the speakers of two languages, which are competing against each other to be saved from destruction, attract more speakers and so on, using two nonlinear stochastic parabolic equations. Four factors including the status of the languages and the growth rates of the populations are considered as the control variables (which can be controlled by the speakers 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 language 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.
