期刊
APPLIED MATHEMATICAL MODELLING
卷 78, 期 -, 页码 601-626出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.10.013
关键词
Stochastic chemostat model; Stochastic near-optimal control; Hamiltonian function; Adjoint equation; Sufficient and necessary conditions
资金
- National Natural Science Foundation of China [11771044, 11871007]
Near-optimal controls are as important as optimal controls for both theory and applications. Meanwhile, using inhibitor to control harmful microorganisms and ensure maximum growth of beneficial microorganisms (target microorganisms) is a very interesting topic in the chemostat. Thus, in this paper, we consider a stochastic chemostat model with non-zero cost inhibiting in finite time. The near-optimal control problem was constructed by minimizing the number of harmful microorganisms and minimizing the cost of inhibitor. We find that the Hamiltonian function is key to estimate objective function, and according to the adjoint equation, we obtain some error estimations of the near-optimality. Finally, we establish sufficient and necessary conditions for stochastic near-optimal controls of this model and numerical simulations and some conclusions are given. (C) 2019 Elsevier Inc. All rights reserved.
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