Tracking Control for Competing Multi-Species Population Dynamics governed by Integro-PDEs
Populations that are encountered in ecology, epidemics, or biotechnology, do not only interact over time but also age over time. They are modeled as age-structured partial differential equations, where age is the space variable. Involving integrals over age, they are in fact integro-partial differential equations. Population dynamics can be observed in chemostat reactors, where harvesting is used as input to regulate population densities to track desired reference trajectories. Up to date, such models have only been considered as single input, single output systems, imposing strict constraints on reference trajectories when multiple species are involved. We present a novel model for two competing populations in a cascaded chemostat setup, allowing for an independent tracking control of each species. The control is implemented in a two degree of freedom structure based on the linearized system, with an inversion-based feedforward control and a robust feedback law. The designed control is able to track sinusoidal reference trajectories around the steady state with low error, underlining the great potential of model-based control in the chemostats.
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