Affiliations: [a] Institute of System Science, Northeastern University, Shenyang, Liaoning Province, China
| [b] School of Mathematics, Jilin Normal University, Siping, Jilin Province, China
Correspondence:
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Corresponding author. Qingling Zhang, Institute of System Science, Northeastern University, Shenyang, Liaoning
Province 110819, China. E-mail: qlzhang@mail.neu.edu.cn.
Abstract: In this paper, the optimal guaranteed cost control problem of a single species model with stage structure is studied by fuzzy methods. The non-linear harvesting model in a toxic environment is established, and the toxin considered has the characteristics of growth and reproduction. Furthermore, for the reason of practical problems, in which the period of production is a finite time and the biomass and toxin should be controlled into some range, the guaranteed cost controller is designed based on fuzzy models. While controlling the biomass concentration achieved the specified range, the controller in this paper eliminated the toxin entirely or controlled the toxin in traces concentration according the actual demand of different environment. Finally, a practical example is carried out to illustrate the feasibility of designed controller in the case of non-toxin and traces of toxin, respectively.
