Near‐optimal control of a stochastic vegetation‐water system with reaction diffusion

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.