This paper is focused on adaptively controlling a linear infinite-dimensional system to cause
it to track a finite-dimensional reference model. Given a linear continuous-time infinite-
dimensional plant on a Hilbert space and disturbances of known waveform but unknown
amplitude and phase, we show that there exists a stabilizing direct model reference adaptive
control law with certain disturbance rejection and robustness properties. The plant is
described by a closed, densely defined linear operator that generates a continuous …

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a
finite-dimensional reference model. Given a linear continuous-time infinite-dimensional
plant on a Hilbert space with disturbances of known waveform but unknown amplitude and
phase, we show that there exists a stabilizing direct model reference adaptive control law
with the properties of certain disturbance rejection and robustness. The plant is described by
a closed, densely defined linear operator that generates a continuous semigroup of …