Abstract
We study a chemostat model with two organisms using Lyapunov function methods. Using a linear feedback control of the dilution rate and an appropriate time-varying substrate input concentration, we produce a locally exponentially stable oscillatory behavior for the species concentrations, meaning all trajectories of the chemostat that stay near the oscillatory reference trajectory are actually attracted to the reference trajectory exponentially fast. We also obtain a globally stable oscillatory reference trajectory for the species concentrations, using a nonlinear feedback control depending on the dilution rate and the substrate input concentration. This guarantees that all trajectories for the closed loop chemostat dynamics are attracted to the reference trajectory. We demonstrate the efficacy of our method using a numerical simulation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.