Abstract.
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.
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Received: 1 November 2001 / Revised version: 19 August 2002 / Published online: 19 November 2002
Mathematics Subject Classification (2000): 34H05, 34D23, 93C10
Keywords or phrases: Chemostat – Feedback control – Coexistence
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De Leenheer, P., Smith, H. Feedback control for chemostat models. J. Math. Biol. 46, 48–70 (2003). https://doi.org/10.1007/s00285-002-0170-x
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DOI: https://doi.org/10.1007/s00285-002-0170-x