Robust Adaptive Control with Disturbance Rejection for Linear Infinite Dimensional Systems

Abstract

Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. 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. To illustrate the utility of the control law, we apply the results to a partial differential equation example of an unstable diffusion system.