Title: Yield Trajectory Tracking for Hyperbolic Age-Structured Population Systems,
Abstract: For population systems modeled by age-structured hyperbolic partial
differential equations (PDEs) that are bilinear in the input and evolve with a
positive-valued infinite-dimensional state, global stabilization of constant
yield set points was achieved in prior work. Seasonal demands in
biotechnological production processes give rise to time-varying yield
references. For the proposed control objective aiming at a global attractivity
of desired yield trajectories, multiple non-standard features have to be
considered: a non-local boundary condition, a PDE state restricted to the
positive orthant of the function space and arbitrary restrictive but physically
meaningful input constraints. Moreover, we provide Control Lyapunov Functionals
ensuring an exponentially fast attraction of adequate reference trajectories.
To achieve this goal, we make use of the relation between first-order
hyperbolic PDEs and integral delay equations leading to a decoupling of the
input-dependent dynamics and the infinite-dimensional internal one.
Furthermore, the dynamic control structure does not necessitate exact knowledge
of the model parameters or online measurements of the age-profile. With a
Galerkin-based numerical simulation scheme using the key ideas of the
Karhunen-Loève-decomposition, we demonstrate the controller's performance.