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Feedback control for chemostat models. (English) Zbl 1015.92046
Summary: It is shown that a chemostat with two organisms can be made coexistent by means of feedback control of the dilution rate. Remaining freedom in the feedback law can be used to guarantee robustness or improve particular performance indices. Unfortunately, a topological property prevents coexistence by feedback control for chemostats with more than two organisms. We apply our results to control bioreactors aimed at producing commercial products through genetically altered organisms. In all our results the coexistence takes its simplest form: a global asymptotically stable equilibrium point in the interior of the non-negative orthant.

MSC:
92D40Ecology
93B52Feedback control
93C95Applications of control theory
92C40Biochemistry, molecular biology
34D23Global stability of ODE