Premium
Near‐optimal control of a stochastic vegetation‐water system with reaction diffusion
Author(s) -
Pan Shiliang,
Zhang Qimin,
Anke MeyerBaese
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6346
Subject(s) - mathematics , optimal control , a priori and a posteriori , vegetation (pathology) , stochastic control , mathematical optimization , reaction–diffusion system , maximum principle , probability density function , hamiltonian (control theory) , stochastic modelling , mathematical analysis , statistics , medicine , philosophy , epistemology , pathology
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.