Tracking-control for age-structured population dynamics with self-competition governed by integro-PDEs. (November 2021)

• Record Type: Journal Article
• Authors: Kurth, Anna-Carina; Schmidt, Kevin; Sawodny, Oliver
• Is Part Of: Automatica. Volume 133(2021)
• Publication Date: 2021-11
• Subjects: Distributed parameter systems -- Biocybernetics -- Partial differential equations -- Exponentially stable; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109850
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The dynamics of population systems can be observed in chemostat reactors under laboratory conditions. The modeling of these kind of systems leads to a nonlinear, hyperbolic, first-order integro-partial differential equation with integral boundary condition. Hereby, the state is the population density and the input is the restricted dilution rate. Through an appropriate choice of the steady-state input a generalized spectral analysis is carried out. By using this result and a nonlinear mapping the partial differential equation is split into an input/output-normal form and an integral delay equation. Due to the global exponential stability of the integral delay equation, a feedforward controller is designed for the input/output-normal form. This is complemented with a feedback controller to compensate the influence of the integral delay equation on the output. The global exponential attractivity of reference trajectories meeting certain requirements is proven. Simulations show the performance of the controller saturated to the input constraints in dependency of the controller settings.