Output regulation for linear distributed-parameter systems using finite-dimensional dual observers

In this article, the solution of the output regulation problem is considered for linear infinite-dimensional systems where the outputs to be controlled cannot be measured. It is shown that this problem can be solved by a finite-dimensional dual observer that is directly implementable so that the separation principle can be applied for the stabilization as in finite dimensions. A parametric design of these dual observers is proposed for Riesz-spectral systems that allows to achieve a low controller order and a desired control performance for the closed-loop system. The presented results are illustrated by determining a finite-dimensional regulator for an Euler–Bernoulli beam with Kelvin–Voigt damping that achieves tracking for steplike reference inputs and that asymptotically rejects sinusoidal disturbances.