Direct adaptive control for persistent disturbance rejection in linear infinite dimensional systems

Given a linear continuous-time infinite-dimensional plant on a Hilbert space and persistent disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with disturbance rejection and robustness properties. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or disturbance estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.