Feedback control for chemostat models.
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.
De Leenheer
Patrick
P
Arizona State University, Department of Mathematics, Tempe, AZ 85287, USA. leenheer@math.la.asu.edu
Smith
Hal
H
D001419:Bacteria / Q000254:growth & development; D019149:Bioreactors / Q000382:microbiology*; D005246:Feedback; D008954:Models, Biological; D030781:Organisms, Genetically Modified / Q000254:growth & development; D011157:Population Dynamics