In this article, we study the near‐optimal control of a class of stochastic vegetation‐water model. The near‐optimal control is one problem in which the density of vegetation and water is higher at the lowest cost. We have provided a priori estimates of the vegetation and water densities and obtained the sufficient and necessary conditions for the system's near‐optimal control problem by applying the maximum condition of the Hamiltonian function and the Ekeland principle. A numerical simulation is presented to verify our theoretical results.

中文翻译：

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具有反应扩散的随机植被-水系统的近最优控制

在本文中，我们研究了一类随机植被-水模型的近最优控制。接近最佳控制是一个问题，其中植物和水的密度较高，成本最低。我们通过应用汉密尔顿函数和Ekeland原理的最大条件，提供了植被和水密度的先验估计，并为系统的接近最优控制问题获得了充要条件。进行了数值模拟，以验证我们的理论结果。