Further results on stabilization of periodic trajectories for a chemostat with two species
We discuss an important class of problems involving the tracking of prescribed trajectories in the chemostat model.We provide new tracking results for chemostats with two species and one limiting substrate, based on Lyapunov function methods. In particular, we use a linear feedback control of the dilution rate and an appropriate time-varying substrate input concentration to produce a locally exponentially stable oscillatory behavior. This means that all trajectories for the nutrient and corresponding species concentrations in the closed loop chemostat that stay near the oscillatory reference trajectory are 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. Finally, we construct an explicit Lyapunov function for the corresponding global error dynamics.We demonstrate the efficacy of our method in a simulation. © 2008 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Automatic Control
Mazenc, F., Malisoff, M., & Harmand, J. (2008). Further results on stabilization of periodic trajectories for a chemostat with two species. IEEE Transactions on Automatic Control, 53 (SPECIAL ISSUE), 66-74. https://doi.org/10.1109/TAC.2007.911315